Relations between $K_2$ and Galois cohomology

DOI10.1007/BF01390012zbMath0359.12011WikidataQ56209985 ScholiaQ56209985MaRDI QIDQ1238847

Publication date: 1976

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142421

Mathematics Subject Classification ID

Galois cohomology (12G05) (K)-theory of global fields (11R70) Symbols and arithmetic ((K)-theoretic aspects) (19F15) Galois cohomology (11R34)

Related Items

$K_2$ and the Greenberg conjecture in multiple $\mathbb Z_p$-extensions, Finite $\Lambda$-submodules of Selmer groups of Abelian varieties over cyclotomic $\mathbb Z_p$-extensions., Tame kernels of pure cubic fields, The $E_{2}$-term of the $K(n)$-local $E_{n}$-Adams spectral sequence, The 2-Sylow subgroup of $K_2O_F$ for certain quadratic number fields, A genus formula for the wild étale kernel, Motivic cohomology with $\mathbb Z/2$-coefficients, On Tate-Shafarevich groups over Galois extensions, $p$-adic étale cohomology, Algebraic number fields, Algebraic cycles and values of L-functions. II, The structure of the 2-Sylow subgroup of $K_ 2({\mathfrak o})$. II, The Merkuriev--Suslin theorem for any semi-local ring, Hirzebruch-Zagier cycles and twisted triple product Selmer groups, Continuous étale cohomology, The extended Bloch groups of biquadratic and dihedral number fields, Central extensions of simply connected algebraic groups and Galois cohomology, The 3-Sylow subgroup of the tame kernel of real number fields, Cup product, étale capitulation kernels and generalized Greenberg conjecture, A cohomological transfer map for profinite groups, Über gewisse Galoiscohomologiegruppen, Splitting in the $K$-theory localization sequence of number fields, Hermitian $K$-theory and 2-regularity for totally real number fields, Support problem for the intermediate Jacobians of $l$-adic representations., A generalization of Darmon's conjecture for Euler systems for general $p$-adic representations, On the cohomology of semi-stable $p$-adic Galois representations, K-théorie des anneaux d'entiers de corps de nombres et cohomologie etale, On the 3-rank of tame kernels of certain pure cubic number fields, Continuous group actions on profinite spaces, On special elements in higher algebraic $K$-theory and the Lichtenbaum-Gross conjecture, Transfer in Galois cohomology commutes with transfer in the Milnor ring, On regular number fields, Higher analogues of Stickelberger's theorem., On the structure of the $K_ 2$ of the ring of integers in a number field, The wild kernel of exceptional number fields., A cohomological study of the 2-primary part of $K_2{\mathcal O})$, The densities for 3-ranks of tame kernels of cyclic cubic number fields, Quadratic extensions with elementary abelian $K_ 2(O)$, Torsion zero-cycles and étale homology of singular schemes, On torsion in $K_ 2$ of fields, On the $p$-rank of tame kernel of number fields, On the torsion in $K_2$ of a field, On the cycle map for torsion algebraic cycles of codimension two, Milnor $K$-groups attached to elliptic curves over a $p$-adic field, On the corestriction of $p^ n$-symbol, Generating the tame and wild kernels by Dennis-Stein symbols, Tame kernels of cubic and sextic fields, Class number parity and unit signature, Some examples of torsion in the Griffiths group, Iwasawa theory and $p$-adic heights, Relative Milnor $K$-theory, $K_ 2$ of rings of algebraic integers, Finding non-trivial elements in $K_ 2({\mathcal O}_ F)$ for imaginary quadratic number fields $F$, Two comparison theorems in étale cohomology; applications, The period-index obstruction for elliptic curves, The 2-Sylow subgroup of $K_{2} O_{F}$ for number fields $F$, The formula of 8-ranks of tame kernels, Étale analogs of $p$-tower class field, Weights in arithmetic geometry, Fine Selmer groups of elliptic curves over $p$-adic Lie extensions, 2-group of positive classes of a number field and wild kernel of $K$-theory., Euler system for Galois deformations., An expression for primes and its application to $K_2\mathbb Q$, Bounds for étale capitulation kernels, A short remark on the Merkurjev-Suslin theorem, Quadratic extensions of number fields with elementary abelian 2-prim $K_2(O_F)$ of smallest rank, Wild kernels and divisibility in $K$-groups of global fields, Galois cohomology of a number field is Koszul, On finite layers of $\mathbb{Z}_l$-extensions and $K_2$, A Riemann-Roch type theorem for the Witt and Milnor rings of a field, Triviality of the 2-rank of the Hilbert kernel, The analogue of the Gauss class number problem in motivic cohomology, On duality and Iwasawa descent, $\ell $-adic class field theory for regular local rings, Bounds for étale capitulation kernels. II, Corestriction principle in non abelian Galois cohomology, Systèmes d'Euler $p$-adiques et théorie d'Iwasawa. ($p$-adic Euler systems and Iwasawa theory.), The construction of weight-two arithmetic cohomology, Capitulation for even $K$-groups in the cyclotomic $\mathbb Z_p$-extension, Iterated homotopy fixed points for the Lubin-Tate spectrum, Abel-Jacobi mappings and finiteness of motivic cohomology groups, Reflexion theorems, 8-ranks of $K_2$ of rings of integers in quadratic number fields, On Iwasawa theory of crystalline representations, The sign of the functional equation of the $L$-function of an orthogonal motive, Control theorem for Bloch-Kato's Selmer groups of $p$-adic representations, L'anneau de Milnor d'un corps local à corps résiduel parfait, Fields with vanishing $K_ 2$. Torsion in $H^ 1(X,K_ 2)$ and $Ch^ 2(X)$, Class fields of abelian extensions of $\mathbb Q$, Algebraic $K$-theory and the norm residue homomorphism, Isotropy of quadratic forms over function fields of $p$-adic curves, Generic algebras with involution of degree $8m$., On $\mathbb{Z}_ p$-torsion of some Galois modules, Kolyvagin's method for Chow groups and Kuga-Sato varieties, On tame kernel and class group in terms of quadratic forms., Iwasawa theory of $p$-adic representations over a local field, Initial stage of a $\mathbb{Z}_ \ell$-extension, A conjecture on a class of elements of finite order in $K_2F_{\mathfrak p}$, Tame kernels and further 4-rank densities., Remarks on $K_ 2$ of number fields, Herr‐complexes in the Lubin–Tate setting, Right‐angled Artin pro‐p$p$ groups, Asymptotic behavior of class groups and cyclotomic Iwasawa theory of elliptic curves, Level compatibility in Sharifi’s conjecture, Motivic cohomology, Abelian geometric fundamental groups for curves over a $p$-adic field, Modular forms of half-integral weight on exceptional groups, On the structure of even $K$-groups of rings of algebraic integers, Unnamed Item, $\Phi$-$\Gamma$-modules for families of Galois representations, The 2-Sylow subgroup of the wild kernel of exceptional number fields, On $K_2$ of finite dimensional division algebras over arithmetical fields, On the 4-rank of the tame kernel $K_2(\mathcal O)$ in positive definite terms, Dyadic ideal, class group, and tame kernel in quadratic fields, Étale cohomology, cofinite generation, and $p$-adic $L$-functions, On $K_2$ of finite dimensional division algebras over arithmetical fields, Galois symbol maps for abelian varieties over a $p$-adic field, Syntomic complexes and p-adic étale Tate twists, Norm index formula for the Tate kernels and applications, Oriented pro-$\ell$ groups with the Bogomolov-Positselski property, TRANSPORT PARALLÈLE ET CORRESPONDANCE DE SIMPSON -ADIQUE, The `life machine': a quantum metaphor for living matter, Galois descent and $K_ 2$ of number fields, SOME DIOPHANTINE EQUATIONS OVER AND WITH APPLICATIONS TO OF A FIELD, Unnamed Item, The 3-adic regulators and wild kernels, Analogues supérieurs du noyau sauvage, On Browkin's conjecture about the elements of order five in $K_2(\mathbb Q)$, Totally Ramified Valuations on Finite-Dimensional Division Algebras, Selmer groups as flat cohomology groups, ÉTALE MOTIVIC COHOMOLOGY AND ALGEBRAIC CYCLES, Les nombres de Tamagawa locaux et la conjecture de Bloch et Kato pour les motifs sur un corps abélien, Codescent in étale $K$-theory and number fields, On the $p$-adic height of Heegner cycles, Integral motives and special values of zeta functions, The weight two $K$-theory of fields, Effect of increasing the ramification on pseudo-deformation rings, Unnamed Item, On the cyclotomic norms and the Leopoldt and Gross-Kuz'min conjectures, Induced orthogonal representations of Galois groups, Galois-theoretic features for 1-smooth pro-p groups, Torsion orders of Fano hypersurfaces, VALUES AT s = -1 OF L-FUNCTIONS FOR MULTI-QUADRATIC EXTENSIONS OF NUMBER FIELDS, AND THE FITTING IDEAL OF THE TAME KERNEL, The indecomposable $K_3$ of fields, La théorie de Kummer et le $K_2$ des corps de nombres, Explicit Chabauty-Kim theory for the thrice punctured line in depth 2, On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field, Divisibility results for zero-cycles, The Stickelberger splitting map and Euler systems in the $K$-theory of number fields, The Structure of the Tame Kernels of Quadratic Number Fields (III), The indecomposable 𝐾₃ of fields, Milnor $K$-theory of $p$-adic rings, A Note on the 4-Rank Densities ofK₂O_Ffor Quadratic Number FieldsF, Steinberg symbols and reciprocity sheaves, A finiteness theorem for the Brauer group of abelian varieties and 𝐾3 surfaces, Profinite groups with a cyclotomic $p$-orientation, Tame kernels of cubic cyclic fields, On the structure of Selmer and Shafarevich–Tate groups of even weight modular forms, An example of algebraic cycles with nontrivial Abel-Jacobi images, Higher degree tame Hilbert-symbol equivalence of number fields, The p-adic Coates–Sinnott Conjecture over maximal orders, Koszul algebras and quadratic duals in Galois cohomology, Computing generators of the tame kernel of a global function field, Normes universelles et conjecture de Greenberg, Cohomology of algebraic varieties over the maximal cyclotomic extension of a global field, Potentially diagonalisable lifts with controlled Hodge-Tate weights, On λ-invariants of number fields and étale cohomology, On tame kernels and ideal class groups, On $p$-rationality of $\mathbb{Q}(\zeta_{2l+1})^+$ for Sophie Germain primes $l$, On the elements of prime power order in $K_2(\mathbb Q)$, Tate kernels and capitulation, Good reduction of the Brauer–Manin obstruction, On odd prime numbers dividing the order of K₂(σ), Cohomology and torsion cycles over the maximal cyclotomic extension, Reflection Theorems and the Tame Kernel of a Number Field, A genus formula for the positive étale wild kernel, Elements of prime power order in $K_{2}(\mathbb Q)$, A Remark onK₂of the Rings of Integers of Totally Real Number Fields, A New Construction of Noncrossed Product Algebras, Algebraic K-theory, Higher wild kernels and divisibility in the $K$-theory of number fields, Reflection theorems and the $p$-Sylow subgroup of $K_{2}O_F$ for a number field $F$, The theory of Coleman power series for 𝐾₂, Homotopy fixed points for $L_{K(n)}(E_{n}\land X)$ using the continuous action, Unnamed Item, Tame kernels for biquadratic number fields, An idelic approach to the wild kernel, Étale wild kernels of exceptional number fields, Logarithmic approach of the étale wild kernels of number fields., Unnamed Item, On higher fitting ideals of certain Iwasawa modules associated with Galois representations and Euler systems, On universal norms and the first layers of $\mathbb Z_p$-extensions of a number field, The Tame Kernel of Multiquadratic Number Fields, Memories of Kenkichi Iwasawa, On a torsion analogue of the weight-monodromy conjecture, Asymptotic lower bound of class numbers along a Galois representation, MILNOR K-GROUP ATTACHED TO A TORUS AND BIRCH–TATE CONJECTURE, A Tate duality theorem for local Galois symbols. II. The semi-abelian case, A BSD formula for high-weight modular forms, Unnamed Item, A Finiteness Theorem in the Galois Cohomology of Algebraic Number Fields, Ranks of Selmer groups in an analytic family, Syntomic cohomology and Beilinson’s Tate conjecture for 𝐾₂, Torsion zero-cycles on the self-product of a modular elliptic curve, Statistics of $K$-groups modulo $p$ for the ring of integers of a varying quadratic number field, Four-fold Massey products in Galois cohomology, On 2-Sylow Subgroups of Tame Kernels, Computing Néron–Severi groups and cycle class groups, Galois action on VOA gauge anomalies, Generalized Steinberg relations, Linear relations and arithmetic on abelian schemes, Galois cohomology for Lubin-Tate $(\varphi_q,\Gamma_{LT})$-modules over coefficient rings, On 3-Nilpotent Obstructions to π1 Sections for $$ \mathbb{P}^{1}_\mathbb{Q}$$−{0,1, $$\infty$$}, Overview of Some Iwasawa Theory, Modular Symbols in Iwasawa Theory, On the splitting of the exact sequence, relating the wild and tame kernels, Théorie d’Iwasawa des unités de Stark et groupe de classes, Local to global principle for semiabelian varieties isogenous to the product of an abelian variety and a torus

Cites Work

Relations between \(K_2\) and Galois cohomology