Witt vectors. Part 1 (Q3053864)

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Language	Label	Description	Also known as
English	Witt vectors. Part 1	scientific article

Statements

scholarly article

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Witt vectors. Part 1 (English)

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Michiel Hazewinkel

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Handbook of Algebra - Volume 6

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publication date

30 October 2010

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full work available at URL

https://arxiv.org/abs/0804.3888

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zbMATH Keywords

Witt vectors

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Witt polynomials

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MaRDI profile type

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Inner plethysm in the representation ring of the general linear group.

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On the structure of the Hopf representation ring of the symmetric groups.

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Explicit formulae for the Hilbert symbol of a formal group over the Witt vectors

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GALOIS MODULI OF PERIOD $p$ GROUP SCHEMES OVER A RING OF WITT VECTORS

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The image of the Galois group for some crystalline representations

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MODULAR REPRESENTATIONS OF THE GALOIS GROUP OF A LOCAL FIELD, AND A GENERALIZATION OF THE SHAFAREVICH CONJECTURE

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Grothendieck groups of bundles on varieties over finite fields

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Cyclic fields of degree 𝑝ⁿ over 𝐹 of characteristic 𝑝

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Endomorphisms of finitely generated projective modules over a commutative ring

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The Grothendieck ring of the category of endomorphisms

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Erratum to ``K-theory of endomorphisms''

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Splitting necklaces

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The Borsuk-Ulam Theorem and Bisection of Necklaces

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Formal groups arising from algebraic varieties

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Non-vanishing of alternants

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EXPONENTIAL ISOMORPHISMS FOR λ-RINGS

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Group representations, \(\lambda\)-rings and the \(J\)-homomorphism

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A functorial property of nested Witt vectors

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Déformations des p-groupes finis à un schéma formel sans p-torsion

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Quasisymmetric functions from a topological point of view

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Applications of the lifting from \(\text{char } p\) of some rational \(n\)-fold

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On Witt vectors and periodic group-varieties

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Difference equations in Witt vectors

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Integer-valued difference rational functions over Witt vectors

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L'automorphisme de Frobenius des vecteurs de Witt

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Model theory of the Frobenius on the Witt vectors

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Approximation for Frobenius algebraic equations in Witt vectors

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Limites de représentations cristallines

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A combinatorial outlook on symmetric functions

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Une combinatoire du pléthysme. (Combinatorics of plethysm)

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On Co-Groups in the Category of Graded Algebras

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On Witt vector cohomology for singular varieties

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A Stickelberger theorem for p-adic Gauss sums

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Universal deformation rings and dihedral 2-groups

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Universal deformation rings and dihedral defect groups

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Universal deformation rings and Klein four defect groups

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Deformations with respect to an algebraic group.

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Necklace Lie algebras and noncommutative symplectic geometry.

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S-Operations in Representation Theory

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The basic geometry of Witt vectors. I: The affine case

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Galois theory and integral models of Λ-rings

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Plethystic algebra

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Asymptotics of a sequence of Witt vectors

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On \(\lambda\)-rings and the \(K\)-theory of infinite loop spaces

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The restriction of the outer plethysm to a young subgroup

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Construction de représentations p-adiques semi-stables

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Schémas en groupe et modules filtrés

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Topologie log-syntomique, cohomologie log-cristalline et cohomologie de Čech

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MSS sequences, colorings of necklaces, and periodic points of \(f(z)=z^ 2-2\)

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Witt vectors and equivariant ring spectra applied to cobordism

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Witt vectors and Tambara functors

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Witt vectors which are rational functions

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Réduction des tores déployés par une extension modérément ramifiée. (Reduction of tori split over tamely ramified extensions).

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Operations in Grothendieck Rings and the Symmetric Group

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Integer-valued polynomials

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Representations of the Symmetric Group in Deformations of the Free Lie Algebra

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Plethysm and vertex operators

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Groupes de Lubin-Tate généralises

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La théorie du symbole de restes normiques.

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Commuting polynomials and \(\lambda\)-ring structures on \(\mathbb{Z}[x]\)

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Commutative rings with restricted minimum condition

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On the Structure and Ideal Theory of Complete Local Rings

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Dual numbers, Witt vectors, and Hjelmslev planes

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Feynman identity: a special case revisited

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Vanishing via lifting to second Witt vectors and a proof of an isotriviality result

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Covariant Honda theory

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On the Artin-Hasse Exponential Series

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Singular vectors of quantum group representations for straight Lie algebra roots

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Singular vectors of representations of quantum groups

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Quantum group \(U_q(A_\ell)\) singular vectors in Poincaré-Birkhoff-Witt basis

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Quantum group<i>U</i><sub><i>q</i></sub>(<i>D</i><sub>ℓ</sub>) singular vectors in the Poincaré-Birkhoff-Witt basis

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Irregular <i>Uq</i> <b>(</b>sl(3)<b>)</b> representations at roots of unity via Gel’fand–(Weyl)–Zetlin basis

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Fixed point indices of iterated maps

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Decomposable functors and the exponential principle

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A multinomial identity for Witt vectors

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A characterisation of solvable groups

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Congruence relations characterizing the representation ring of the symmetric group

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The Burnside ring of the infinite cyclic group and its relations to the necklace algebra, \(\lambda\)-rings, and the universal ring of Witt vectors

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On the number of solutions of certain linear Diophantine equations

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A simple proof for a result by Kratzer and Thévenaz concerning the embedding of the Burnside ring into its ghost ring

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On the integrality of the Witt polynomials

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An application of Burnside rings in elementary finite group theory

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The Burnside ring of profinite groups and the Witt vector construction

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NONCOMMUTATIVE SYMMETRIC FUNCTIONS VI: FREE QUASI-SYMMETRIC FUNCTIONS AND RELATED ALGEBRAS

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Norm residue symbol in local number fields

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The Homotopy Theory of Cyclic Sets

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Binomial rings, integer-valued polynomials, and \(\lambda\)-rings

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Constructing Witt-Burnside rings

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Valuation theory

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Projective ideals in Cohen rings

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The real numbers as a wreath product

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On \(\mathbb{Z}_p\)-extensions of commutative rings

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Minimal degree liftings in characteristic 2

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An algorithm for generating necklaces of beads in two colors

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Necklaces of beads in k colors and k-ary de Bruijn sequences

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Cogroups in algebras over an operad are free algebras

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Universelle Eigenschaften der Wittschen Vektoren und der Einseinheitenalgebra einer Potenzreihenalgebra in einer Veränderlichen

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A theorem on flows in networks

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Qsym over Sym is free

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\(r\)-Qsym is free over Sym

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Algèbres de groupe du groupe additif

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Multiplication of matrices and Witt vectors

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Lifting of the binomial coefficients in Witt vectors

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A PBW basis for lusztig’s form of untwisted affine quantum groups

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On \(K_ 3\) of Witt vectors of length two over finite fields

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Noncommutative symmetric functions

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On the deformation of rings and algebras

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On the deformation of rings and algebras. II

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On the deformation of rings and algebras. III

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On the deformation of rings and algebras. IV

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The shuffle bialgebra and the cohomology of commutative algebras

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Analytic Properties of Power Product Expansions

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Vecteurs de Witt non commutatifs et représentabilité de l'homologie modulo \(p\). (Noncommutative Witt vectors and representability of homology modulo \(p\))

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Generalised Witt vectors

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Realizing deformations of curves using Lubin-Tate formal groups

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Unit Witt Vectors

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La théorie des classes de Chern

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Higher \(K\)-theory of toric varieties

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Toric varieties with huge Grothendieck group

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Formal and analytic deformations of the Witt algebra

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The Representation Ring of a Simply Connected Lie Group as a λ-Ring

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Infinite dimensional algebraic geometry: algebraic structures on \(p\)-adic groups and their homogeneous spaces

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On non-commutative extensions of \(G_a\) by \(G_m\) over an \(\mathbb F_p\)-algebra

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The algebra of quasi-symmetric functions is free over the integers

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Cofree coalgebras and multivariable recursiveness.

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Explicit polynomial generators for the ring of quasisymmetric functions over the integers.

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On the Snapper/Liebler-Vitale/Lam theorem on permutation representations of the symmetric group

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Algebras, Rings and Modules

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Representations of the symmetric group, the specialization order, systems and Grassmann manifolds

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Generalized \(t\)-modules

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Witt vectors of non-commutative rings and topological cyclic homology

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On the \(K\)-theory of finite algebras over Witt vectors of perfect fields

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the absolute and relative de rham–witt complexes

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Galois cohomology of Witt vectors of algebraic integers

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Hecke algebras, difference operators, and quasi-symmetric functions

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An analogue of the plactic monoid for binary search trees

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The algebra of multiple harmonic series

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Quasi-shuffle products

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Exponential maps and lambda-rings

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\(\tau\)-rings and wreath product representations

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\(K\)-theory of endomorphism rings and of rings of invariants

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A cohomological construction of Swan representation over the Witt ring. I, II

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Complexe de de\thinspace Rham-Witt et cohomologie cristalline

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GEOMETRY OF DIFFERENTIAL EQUATIONS AND PROJECTIVE REPRESENTATIONS OF THE WITT ALGEBRA

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On the Witt vectors over nonperfect rings

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Representation of Witt vectors by formal power series and its applications

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Free Lie algebras, generalized Witt formula, and the denominator identity

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The Morava \(K\)-theory and Brown-Peterson cohomology of spaces related to \(BP\).

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Power series and \(p\)-adic algebraic closures

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\(\lambda\)-rings and the representation theory of the symmetric group

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Endomorphisms of Monogenic Hopf Algebras

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The Hopf algebra of a uniserial group.

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Monogenic bialgebras over finite fields and rings of Witt vectors

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Monogenic Hopf algebras and local Galois module theory

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Witt subgroups and cyclic Dieudonné modules killed by \(p\).

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Lifting Witt subgroups to characteristic zero

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Modules of Witt vectors

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Witt vectors and complex cobordism

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Kommutative algebraische Gruppen und Ringe

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Noncommutative Symmetric Functions II: Transformations of Alphabets

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NONCOMMUTATIVE SYMMETRIC FUNCTIONS V: A DEGENERATE VERSION OF U<sub>q</sub>(gl<sub>N</sub>)

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Noncommutative symmetric functions. IV: Quantum linear groups and Hecke algebras at \(q=0\)

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The relation between Burnside rings and combinatorial species

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Young diagrams, Schur functions, the Gale-Ryser theorem and a conjecture or Snapper

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DE RHAMWITT COHOMOLOGY FOR A PROPER AND SMOOTH MORPHISM

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A \(q\)-specialization for monomial symmetric functions

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Bemerkungen zur Theorie der bewerteten Körper und Ringe

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Formal group-theoretic generalizations of the necklace algebra, including a \(q\)-deformation

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Symmetric functions, formal group laws, and Lazard's theorem

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Construction of the ring of Witt vectors

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The forms of the Witt group schemes

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The Inner Plethysm of S-Functions

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Products and Plethysms of Characters with Orthogonal, Symplectic and Symmetric Groups

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Arrows, symmetries and representation rings

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Formal moduli for one-parameter formal Lie groups

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The Burnside ring and equivariant stable cohomotopy for infinite groups

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Subfields and automorphism groups of \(p\)-adic fields

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The Generation of Inseparable Fields

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A new class of symmetric functions

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Polynomial functors and wreath products

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Plethysm and conjugation of quasi-symmetric functions.

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On the corestriction of \(p^ n\)-symbol

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Abelian \(p\)-groups of type \((p,\dots,p)\) and \(p\)-adic open discs

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Faithful representations of \(\text{SL}_2\) over truncated Witt vectors.

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The umbral calculus of symmetric functions

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Multisets and the combinatorics of symmetric functions

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Witt vectors and the algebra of necklaces

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On finite limit sets for transformations on the unit interval

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Necklaces, symmetries and self-reciprocal polynomials

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Noncommutative symmetric functions and Laplace operators for classical Lie algebras

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The formal series Witt transform

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Adams operations and \(\lambda\)-operations in \(\beta\)-rings

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λ-Operations in β-rings

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Derivation of Witt vectors with application to \(K_ 2\) of truncated polynomial rings and Laurent series

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On torsion points of formal groups over a ring of Witt vectors

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On the combinatorics of plethysm

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Constructing Sequences of Divided Powers

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A Realization of the Additive Witt Group

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Tensor products of witt hopf algebras

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On the extensions of \(\widehat{W}_n\) by \(\widehat{\mathcal G}^{(\mu)}\) over a \(\mathbb Z_{(p)}\)-algebra

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Outer plethysm, Burnside ring and \(\beta\)-rings

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Classification of the ring of Witt vectors and the necklace ring associated with the formal group law \(X+Y - qXY\)

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Generalized Burnside--Grothendieck ring functor and aperiodic ring functor associated with profinite groups

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Necklace rings and logarithmic functions

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Nested Witt vectors and their \(q\)-deformation

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\(R\)-analogue of the Burnside ring of profinite groups and free Lie algebras

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Closed orbits of gradient flows and logarithms of non-abelian Witt vectors

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The Whitehead group of the Novikov ring

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Algebraic properties of necklace rings

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The weight decomposition of Hopf algebras

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Lambda-anneaux non commutatifs

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Deformed Heisenberg algebra with reflection

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Noncommutative p-adic rings and Witt vectors with coefficients in a separable algebra

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An asymptotic equality for the number of necklaces in a shuffle-exchange network

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Arithmetic and growth of periodic orbits

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On symmetric functions related to Witt vectors and the free Lie algebra

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Free Lie algebra and lambda-ring structure

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A combinatorial overview of the Hopf algebra of MacMahon symmetric functions.

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Plethystic Hopf algebras.

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Continuous derivations of the ring of Witt-vectors

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Power Operations on the Burnside Ring

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Combinatorial Properties of Matrices of Zeros and Ones

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On the degeneration of étale \(\mathbb Z/p\mathbb Z\) and \(\mathbb Z/p^2\mathbb Z\)-torsors in equal characteristic \(p>0\)

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Local André-Oort conjecture for the universal abelian variety

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A Hopf-algebra approach to inner plethysm

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Zyklische algebraische Funktionenkörper vom Grade pn über endlichem Konstantenkörper der Charakteristik p.

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Groupes affines, commutatifs, unipotents sur un corps non parfait

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Some Calabi–Yau threefolds with obstructed deformations over the Witt vectors

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The $T^1$-lifting theorem in positive characteristic

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The Lubin-Tate theory for formal power series fields with finite coefficient fields

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A note on extensions of algebraic and formal groups. III

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On the deformations of Witt groups to tori. II

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Bipolynomial Hopf algebras \(H^*(BSU;\mathbb{Z})\) et al

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Erratum: ''Representatives for P-typical curves''

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\(\lambda\)-Ringstrukturen auf dem Burnsidering der Permutationsdarstellungen einer endlichen Gruppe

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Security in Communication Networks

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The Burnside algebra of a finite group

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A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes

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On \(p\)-adic monodromy

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Products of Witt groups

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Hodge-Witt cohomology of complete intersections

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On the structure of commutative affine group schemes over a non-perfect field

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Representable Functors and Operations on Rings

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On the Kawamata-Viehweg vanishing theorem for a surface in positive characteristic

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Quantum quasi-symmetric functions and Hecke algebras

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Ramification groups in Artin-Schreier-Witt extensions

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Transformation groups

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Transformation groups and representation theory

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Geometric modules over the Burnside ring

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Outer plethysms and \(\lambda\)-rings

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Hopf algebra of class functions and inner plethysms

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The free \(\beta{}\)-ring on one generator

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Polynomial operations from Burnside rings to representation functors

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On the elementary theory of rings of Witt vectors with a multiplicative set of representatives for the residue field

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Aperiodic rings, necklace rings and Witt vectors. II

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Verschiebung and Frobenius operators

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Aperiodic rings, necklace rings, and Witt vectors

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Chain Conditions on Convolution Rings

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Convolution Rings

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Necklace rings and their radicals

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Anneaux De Valuation Discrete Complets non Commutatifs

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Homogeneous weights and exponential sums.

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A relationship between the Hilbert and Witt symbols.

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Unobstructed modular deformation problems

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Generalized local class field theory. II: Existence theorem. III: Second form of existence theorem. Structure of analytic groups. IV: Cardinalities

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Nichtprime Cohen-Ringe

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Lambda-rings, binomial domains, and vector bundles over cp(∞)

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Der Existenzsatz für abelsche Funktionenkörper.

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Konstruktion von galoisschen Körpern der Charakteristik p zu vorgegebener Gruppe der Ordnung pf.

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\(p\)-Algebren und Pfaffsche Formen

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Cohomology of \(\lambda\)-rings

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Deformation Theory of Modules

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Moduli space of filtered \(\lambda\)-ring structures over a filtered ring.

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The generalized Burnside ring of a finite group

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Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$

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Witt-like algebras and their<i>q</i>-analogues

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On Maximally Central Algebras

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Symmetric function products and plethysms and the boson-fermion correspondence

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Théorie de Dieudonné sur un anneau de valuation parfait

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Natural Endomorphisms of Burnside Rings

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Operations on ring structures preserved by normalized automorphisms of group rings

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Cohomology, hyperalgebras, and representations

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The Action of the Morava Stabilizer Group on the Lubin-Tate Moduli Space of Lifts

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ELLIPTIC MODULES

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On certain types of \(p\)-adic representations of the Galois group of a local field; construction of a Barsott-Tate ring.

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Algebraic Rings

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Schemata over local rings

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On the de Rham–Witt complex in mixed characteristic

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Cyclic polytopes and the \(K\)-theory of truncated polynomial algebras

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A q-analog for the virasoro algebra

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Abelian extensions of an absolutely unramified local field with general residue field

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De Rham-Witt cohomology and displays

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Deformations of formal groups and stable homotopy theory

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Hopf Algebras and Multiplicative Fibrations, I

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Hopf Algebras and Multiplicative Fibrations II

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Deformations and liftings of finite, commutative group schemes

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Arithmetic of formal groups and applications. I: Universal norm subgroups

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Etude de la catégorie des algèbres de Hopf commutatives connexes sur un corps. (Study of the category of connected Abelian Hopf algebras over a field)

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On the deformation of Artin-Schreier to Kummer

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EXEMPLES DE VARIÉTÉS PROJECTIVES EN CARACTÉRISTIQUE p NON RELEVABLES EN CARACTÉRISTIQUE ZÉRO

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Unstable \(K\)-cohomology algebra is a filtered \(\lambda\)-ring

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On \(\lambda\)-rings and topological realization

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Polynomial functions and permutation polynomials over some finite commutative rings

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Witt Rings and Permutation Polynomials

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Identifiers

zbMATH Open document ID

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10.1016/S1570-7954(08)00207-6

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

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