Witt vectors. Part 1

DOI10.1016/S1570-7954(08)00207-6zbMath1221.13036arXiv0804.3888WikidataQ56609534 ScholiaQ56609534MaRDI QIDQ3053864

Michiel Hazewinkel

Publication date: 30 October 2010

Published in: Handbook of Algebra - Volume 6 (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.3888

zbMATH Keywords

Witt vectorsWitt polynomials

Mathematics Subject Classification ID

Related Items (14)

Trace formula for rings of Witt vectors ⋮ On \(\pi\)-exponentials. II: Closed formula for the index ⋮ Axiomatic theory of Burnside rings. I ⋮ A universal Hochschild-Kostant-Rosenberg theorem ⋮ Commutation and normal ordering for operators on symmetric functions ⋮ Noncommutative motives in positive characteristic and their applications ⋮ The crystalline period of a height one 𝑝-adic dynamical system ⋮ Splitting behavior of \(S_n\)-polynomials ⋮ Witt vectors and \(K\)-theory of automorphisms via noncommutative motives ⋮ Recent developments on noncommutative motives ⋮ 𝐾-theory of endomorphisms via noncommutative motives ⋮ Topological Realisations of Absolute Galois Groups ⋮ Toward a polynomial basis of the algebra of peak quasisymmetric functions ⋮ Weierstrass coefficients of the canonical lifting

Cites Work

• Witt vectors and Tambara functors
• The formal series Witt transform
• Plethystic algebra
• Infinite dimensional algebraic geometry: algebraic structures on \(p\)-adic groups and their homogeneous spaces
• The Burnside ring of the infinite cyclic group and its relations to the necklace algebra, \(\lambda\)-rings, and the universal ring of Witt vectors
• The Burnside ring of profinite groups and the Witt vector construction
• Polynomial functions and permutation polynomials over some finite commutative rings
• The basic geometry of Witt vectors. I: The affine case
• Witt vectors
• The umbral calculus of symmetric functions
• Deformed Heisenberg algebra with reflection
• Necklace Lie algebras and noncommutative symplectic geometry.
• \(R\)-analogue of the Burnside ring of profinite groups and free Lie algebras
• \(\lambda\)-rings and the representation theory of the symmetric group
• On Witt vectors and periodic group-varieties
• Norm residue symbol in local number fields
• A theorem on flows in networks
• \(p\)-Algebren und Pfaffsche Formen
• Representations of the symmetric group, the specialization order, systems and Grassmann manifolds
• Adams operations and \(\lambda\)-operations in \(\beta\)-rings
• On certain types of \(p\)-adic representations of the Galois group of a local field; construction of a Barsott-Tate ring.
• Witt vectors and the algebra of necklaces
• The shuffle bialgebra and the cohomology of commutative algebras
• The generalized Burnside ring of a finite group
• Local André-Oort conjecture for the universal abelian variety
• Covariant Honda theory
• Ramification groups in Artin-Schreier-Witt extensions
• On non-commutative extensions of \(G_a\) by \(G_m\) over an \(\mathbb F_p\)-algebra
• On the extensions of \(\widehat{W}_n\) by \(\widehat{\mathcal G}^{(\mu)}\) over a \(\mathbb Z_{(p)}\)-algebra
• Minimal degree liftings in characteristic 2
• Nested Witt vectors and their \(q\)-deformation
• Classification of the ring of Witt vectors and the necklace ring associated with the formal group law \(X+Y - qXY\)
• \(r\)-Qsym is free over Sym
• On \(\lambda\)-rings and topological realization
• A cohomological construction of Swan representation over the Witt ring. I, II
• A multinomial identity for Witt vectors
• Outer plethysm, Burnside ring and \(\beta\)-rings
• Polynomial operations from Burnside rings to representation functors
• Verschiebung and Frobenius operators
• Explicit polynomial generators for the ring of quasisymmetric functions over the integers.
• Approximation for Frobenius algebraic equations in Witt vectors
• Fixed point indices of iterated maps
• Congruence relations characterizing the representation ring of the symmetric group
• On torsion points of formal groups over a ring of Witt vectors
• An algorithm for generating necklaces of beads in two colors
• Arithmetic of formal groups and applications. I: Universal norm subgroups
• Outer plethysms and \(\lambda\)-rings
• Transformation groups
• Splitting necklaces
• MSS sequences, colorings of necklaces, and periodic points of \(f(z)=z^ 2-2\)
• Une combinatoire du pléthysme. (Combinatorics of plethysm)
• On the combinatorics of plethysm
• Noncommutative p-adic rings and Witt vectors with coefficients in a separable algebra
• Abelian extensions of an absolutely unramified local field with general residue field
• A combinatorial outlook on symmetric functions
• The relation between Burnside rings and combinatorial species
• \(t\)-motives
• The forms of the Witt group schemes
• Representation of Witt vectors by formal power series and its applications
• Cohomology, hyperalgebras, and representations
• \(\tau\)-rings and wreath product representations
• Transformation groups and representation theory
• Erratum to ``K-theory of endomorphisms
• Arrows, symmetries and representation rings
• Polynomial functors and wreath products
• On the Snapper/Liebler-Vitale/Lam theorem on permutation representations of the symmetric group
• Derivation of Witt vectors with application to \(K_ 2\) of truncated polynomial rings and Laurent series
• Nichtprime Cohen-Ringe
• Hopf algebra of class functions and inner plethysms
• On the deformations of Witt groups to tori. II
• On \(\mathbb{Z}_p\)-extensions of commutative rings
• Singular vectors of quantum group representations for straight Lie algebra roots
• An application of Burnside rings in elementary finite group theory
• On \(p\)-adic monodromy
• On the corestriction of \(p^ n\)-symbol
• Asymptotics of a sequence of Witt vectors
• An asymptotic equality for the number of necklaces in a shuffle-exchange network
• Vecteurs de Witt non commutatifs et représentabilité de l'homologie modulo \(p\). (Noncommutative Witt vectors and representability of homology modulo \(p\))
• A simple proof for a result by Kratzer and Thévenaz concerning the embedding of the Burnside ring into its ghost ring
• Witt vectors and complex cobordism
• \(\lambda\)-Ringstrukturen auf dem Burnsidering der Permutationsdarstellungen einer endlichen Gruppe
• Products of Witt groups
• The real numbers as a wreath product
• On the structure of commutative affine group schemes over a non-perfect field
• Projective ideals in Cohen rings
• Continuous derivations of the ring of Witt-vectors
• Groupes de Lubin-Tate généralises
• Kommutative algebraische Gruppen und Ringe
• A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
• Young diagrams, Schur functions, the Gale-Ryser theorem and a conjecture or Snapper
• Erratum: Representatives for P-typical curves
• Necklaces of beads in k colors and k-ary de Bruijn sequences
• Bipolynomial Hopf algebras \(H^*(BSU;\mathbb{Z})\) et al
• Geometric modules over the Burnside ring
• Necklaces, symmetries and self-reciprocal polynomials
• Dual numbers, Witt vectors, and Hjelmslev planes
• Generalised Witt vectors
• Symmetric functions, formal group laws, and Lazard's theorem
• Lifting Witt subgroups to characteristic zero
• Cogroups in algebras over an operad are free algebras
• Formal and analytic deformations of the Witt algebra
• On the elementary theory of rings of Witt vectors with a multiplicative set of representatives for the residue field
• On the Kawamata-Viehweg vanishing theorem for a surface in positive characteristic
• Abelian \(p\)-groups of type \((p,\dots,p)\) and \(p\)-adic open discs
• Operations on ring structures preserved by normalized automorphisms of group rings
• Vanishing via lifting to second Witt vectors and a proof of an isotriviality result
• Hodge-Witt cohomology of complete intersections
• The weight decomposition of Hopf algebras
• Multisets and the combinatorics of symmetric functions
• A Hopf-algebra approach to inner plethysm
• Commuting polynomials and \(\lambda\)-ring structures on \(\mathbb{Z}[x\)]
• Generalized \(t\)-modules
• \(K\)-theory of endomorphism rings and of rings of invariants
• Deformations of formal groups and stable homotopy theory
• Decomposable functors and the exponential principle
• A note on extensions of algebraic and formal groups. III
• Cyclic polytopes and the \(K\)-theory of truncated polynomial algebras
• The algebra of multiple harmonic series
• Noncommutative symmetric functions. IV: Quantum linear groups and Hecke algebras at \(q=0\)
• On \(K_ 3\) of Witt vectors of length two over finite fields
• A relationship between the Hilbert and Witt symbols.
• Formal group-theoretic generalizations of the necklace algebra, including a \(q\)-deformation
• Witt vectors of non-commutative rings and topological cyclic homology
• Endomorphisms of finitely generated projective modules over a commutative ring
• Monogenic Hopf algebras and local Galois module theory
• Faithful representations of \(\text{SL}_2\) over truncated Witt vectors.
• Homogeneous weights and exponential sums.
• Deformations with respect to an algebraic group.
• Cofree coalgebras and multivariable recursiveness.
• Higher \(K\)-theory of toric varieties
• Qsym over Sym is free
• Réduction des tores déployés par une extension modérément ramifiée. (Reduction of tori split over tamely ramified extensions).
• Plethysm and conjugation of quasi-symmetric functions.
• Hecke algebras, difference operators, and quasi-symmetric functions
• Witt subgroups and cyclic Dieudonné modules killed by \(p\).
• Difference equations in Witt vectors
• Cohomology of \(\lambda\)-rings
• Moduli space of filtered \(\lambda\)-ring structures over a filtered ring.
• Plethysm and vertex operators
• Noncommutative symmetric functions
• Aperiodic rings, necklace rings and Witt vectors. II
• Quantum group \(U_q(A_\ell)\) singular vectors in Poincaré-Birkhoff-Witt basis
• Exponential maps and lambda-rings
• On symmetric functions related to Witt vectors and the free Lie algebra
• On the deformation of rings and algebras. IV
• The Grothendieck ring of the category of endomorphisms
• A functorial property of nested Witt vectors
• An analogue of the plactic monoid for binary search trees
• Unstable \(K\)-cohomology algebra is a filtered \(\lambda\)-ring
• A combinatorial overview of the Hopf algebra of MacMahon symmetric functions.
• Integer-valued difference rational functions over Witt vectors
• The Hopf algebra of a uniserial group.
• Toric varieties with huge Grothendieck group
• Realizing deformations of curves using Lubin-Tate formal groups
• Noncommutative symmetric functions and Laplace operators for classical Lie algebras
• Applications of the lifting from \(\text{char } p\) of some rational \(n\)-fold
• On \(\lambda\)-rings and the \(K\)-theory of infinite loop spaces
• Free Lie algebras, generalized Witt formula, and the denominator identity
• On the \(K\)-theory of finite algebras over Witt vectors of perfect fields
• Quasi-shuffle products
• Construction of the ring of Witt vectors
• The Lubin-Tate theory for formal power series fields with finite coefficient fields
• The free \(\beta{}\)-ring on one generator
• De Rham-Witt cohomology and displays
• Feynman identity: a special case revisited
• The Burnside ring and equivariant stable cohomotopy for infinite groups
• On the degeneration of étale \(\mathbb Z/p\mathbb Z\) and \(\mathbb Z/p^2\mathbb Z\)-torsors in equal characteristic \(p>0\)
• Constructing Witt-Burnside rings
• Binomial rings, integer-valued polynomials, and \(\lambda\)-rings
• Inner plethysm in the representation ring of the general linear group.
• On the structure of the Hopf representation ring of the symmetric groups.
• Necklace rings and logarithmic functions
• On the deformation of rings and algebras. II
• Group representations, \(\lambda\)-rings and the \(J\)-homomorphism
• On the Witt vectors over nonperfect rings
• A characterisation of solvable groups
• Deformations and liftings of finite, commutative group schemes
• On the deformation of rings and algebras. III
• Universelle Eigenschaften der Wittschen Vektoren und der Einseinheitenalgebra einer Potenzreihenalgebra in einer Veränderlichen
• 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)
• Valuation theory
• On finite limit sets for transformations on the unit interval
• Generalized Burnside--Grothendieck ring functor and aperiodic ring functor associated with profinite groups
• Non-vanishing of alternants
• Schemata over local rings
• On the deformation of rings and algebras
• Aperiodic rings, necklace rings, and Witt vectors
• On the number of solutions of certain linear Diophantine equations
• Subfields and automorphism groups of \(p\)-adic fields
• Commutative rings with restricted minimum condition
• Generalized local class field theory. II: Existence theorem. III: Second form of existence theorem. Structure of analytic groups. IV: Cardinalities
• Integer-Valued Polynomials
• A Realization of the Additive Witt Group
• Hopf Algebras
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Zyklische algebraische Funktionenkörper vom Grade pn über endlichem Konstantenkörper der Charakteristik p.
• Konstruktion von galoisschen Körpern der Charakteristik p zu vorgegebener Gruppe der Ordnung pf.
• On Maximally Central Algebras
• Bemerkungen zur Theorie der bewerteten Körper und Ringe
• On the Structure and Ideal Theory of Complete Local Rings
• The Generation of Inseparable Fields
• A new class of symmetric functions
• Closed orbits of gradient flows and logarithms of non-abelian Witt vectors
• The Whitehead group of the Novikov ring
• Power series and \(p\)-adic algebraic closures
• Monogenic bialgebras over finite fields and rings of Witt vectors
• The Morava \(K\)-theory and Brown-Peterson cohomology of spaces related to \(BP\).
• On the integrality of the Witt polynomials
• Multiplication of matrices and Witt vectors
• Lifting of the binomial coefficients in Witt vectors
• Grothendieck groups of bundles on varieties over finite fields
• A \(q\)-specialization for monomial symmetric functions
• The algebra of quasi-symmetric functions is free over the integers
• A q-analog for the virasoro algebra
• Plethystic Hopf algebras.
• Free Lie algebra and lambda-ring structure
• Noncommutative Symmetric Functions II: Transformations of Alphabets
• Irregular Uq (sl(3)) representations at roots of unity via Gel’fand–(Weyl)–Zetlin basis
• λ-Operations in β-rings
• Déformations des p-groupes finis à un schéma formel sans p-torsion
• Witt-like algebras and theirq-analogues
• Explicit formulae for the Hilbert symbol of a formal group over the Witt vectors
• Quantum quasi-symmetric functions and Hecke algebras
• Algebraic properties of necklace rings
• Construction de représentations p-adiques semi-stables
• The $T^1$-lifting theorem in positive characteristic
• L'automorphisme de Frobenius des vecteurs de Witt
• Quantum groupU_q(D_ℓ) singular vectors in the Poincaré-Birkhoff-Witt basis
• NONCOMMUTATIVE SYMMETRIC FUNCTIONS V: A DEGENERATE VERSION OF U_q(gl_N)
• Unobstructed modular deformation problems
• Limites de représentations cristallines
• Some Calabi–Yau threefolds with obstructed deformations over the Witt vectors
• Witt Rings and Permutation Polynomials
• Algèbres de groupe du groupe additif
• The image of the Galois group for some crystalline representations
• The Borsuk-Ulam Theorem and Bisection of Necklaces
• La théorie du symbole de restes normiques.
• Cyclic fields of degree 𝑝ⁿ over 𝐹 of characteristic 𝑝
• Der Existenzsatz für abelsche Funktionenkörper.
• NONCOMMUTATIVE SYMMETRIC FUNCTIONS VI: FREE QUASI-SYMMETRIC FUNCTIONS AND RELATED ALGEBRAS
• DE RHAMWITT COHOMOLOGY FOR A PROPER AND SMOOTH MORPHISM
• On the de Rham–Witt complex in mixed characteristic
• Lambda-anneaux non commutatifs
• The Action of the Morava Stabilizer Group on the Lubin-Tate Moduli Space of Lifts
• Analytic Properties of Power Product Expansions
• Symmetric function products and plethysms and the boson-fermion correspondence
• Convolution Rings
• Model theory of the Frobenius on the Witt vectors
• A Stickelberger theorem for p-adic Gauss sums
• On Co-Groups in the Category of Graded Algebras
• Deformation Theory of Modules
• Security in Communication Networks
• Algebraic Rings
• Formal moduli for one-parameter formal Lie groups
• The Burnside algebra of a finite group
• Hopf Algebras and Multiplicative Fibrations, I
• Constructing Sequences of Divided Powers
• Hopf Algebras and Multiplicative Fibrations II
• Representable Functors and Operations on Rings
• EXPONENTIAL ISOMORPHISMS FOR λ-RINGS
• Groupes affines, commutatifs, unipotents sur un corps non parfait
• the absolute and relative de rham–witt complexes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topologie log-syntomique, cohomologie log-cristalline et cohomologie de Čech
• Witt vectors which are rational functions
• Universal deformation rings and Klein four defect groups
• Galois cohomology of Witt vectors of algebraic integers
• On the deformation of Artin-Schreier to Kummer
• Natural Endomorphisms of Burnside Rings
• Combinatorial Properties of Matrices of Zeros and Ones
• The Inner Plethysm of S-Functions
• Products and Plethysms of Characters with Orthogonal, Symplectic and Symmetric Groups
• On the Artin-Hasse Exponential Series
• La théorie des classes de Chern
• EXEMPLES DE VARIÉTÉS PROJECTIVES EN CARACTÉRISTIQUE p NON RELEVABLES EN CARACTÉRISTIQUE ZÉRO
• Unit Witt Vectors
• MODULAR REPRESENTATIONS OF THE GALOIS GROUP OF A LOCAL FIELD, AND A GENERALIZATION OF THE SHAFAREVICH CONJECTURE
• Chain Conditions on Convolution Rings
• Witt vectors and equivariant ring spectra applied to cobordism
• Endomorphisms of Monogenic Hopf Algebras
• The Representation Ring of a Simply Connected Lie Group as a λ-Ring
• On Witt vector cohomology for singular varieties
• Algebras, Rings and Modules
• Galois theory and integral models of Λ-rings
• Quasisymmetric functions from a topological point of view
• Universal deformation rings and dihedral 2-groups
• Universal deformation rings and dihedral defect groups
• The Homotopy Theory of Cyclic Sets
• GALOIS MODULI OF PERIOD $p$ GROUP SCHEMES OVER A RING OF WITT VECTORS
• Complexe de de\thinspace Rham-Witt et cohomologie cristalline
• Théorie de Dieudonné sur un anneau de valuation parfait
• Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
• Anneaux De Valuation Discrete Complets non Commutatifs
• Lambda-rings, binomial domains, and vector bundles over cp(∞)
• Singular vectors of representations of quantum groups
• The restriction of the outer plethysm to a young subgroup
• Operations in Grothendieck Rings and the Symmetric Group
• S-Operations in Representation Theory
• ELLIPTIC MODULES
• Tensor products of witt hopf algebras
• Formal groups arising from algebraic varieties
• Power Operations on the Burnside Ring
• A PBW basis for lusztig’s form of untwisted affine quantum groups
• Schémas en groupe et modules filtrés
• Representations of the Symmetric Group in Deformations of the Free Lie Algebra
• GEOMETRY OF DIFFERENTIAL EQUATIONS AND PROJECTIVE REPRESENTATIONS OF THE WITT ALGEBRA

This page was built for publication: Witt vectors. Part 1