Remarks on \(K_ 2\) of number fields

DOI10.1016/0022-314X(86)90077-6zbMath0589.12010MaRDI QIDQ1073837

Georges Gras

Publication date: 1986

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

number fieldstame kernelHilbert symbols\(K_ 2\)Birch-Tate conjectureGalois p- extensions

Mathematics Subject Classification ID

Zeta functions and (L)-functions of number fields (11R42) (K)-theory of global fields (11R70) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25)

Related Items (27)

Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions ⋮ Norm index formula for the Tate kernels and applications ⋮ Codescent in étale \(K\)-theory and number fields ⋮ On the 2-primary part of tame kernels of real quadratic fields ⋮ Remarks on classical number-theoretic aspects of Milnor–Witt K-theory ⋮ On the structure of even $K$-groups of rings of algebraic integers ⋮ On regular number fields ⋮ On the structure of the \(K_ 2\) of the ring of integers in a number field ⋮ A remark on the positivity of \(K_{2}\). ⋮ Tame kernels of cubic cyclic fields ⋮ A cohomological study of the 2-primary part of \(K_2{\mathcal O})\) ⋮ Quadratic extensions with elementary abelian \(K_ 2(O)\) ⋮ On \(p\)-rationality of \(\mathbb{Q}(\zeta_{2l+1})^+\) for Sophie Germain primes \(l\) ⋮ Cohomology groups of Fermat curves via ray class fields of cyclotomic fields ⋮ Class number parity and unit signature ⋮ On thep²-Rank of Tame Kernels of Quadratic Fields ⋮ A Remark onK₂of the Rings of Integers of Totally Real Number Fields ⋮ Bounds for étale capitulation kernels ⋮ Multi-quadratic \(p\)-rational number fields ⋮ Tate-Shafarevich groups in the cyclotomic \(\hat{\mathbb{Z}} \)-extension and Weber's class number problem ⋮ Addendum: ``Quadratic extensions of number fields with elementary abelian 2-prime \(K_2(O_F)\) of smallest rank ⋮ Computation of 2-groups of narrow logarithmic divisor classes of number fields ⋮ Reflexion theorems ⋮ The p-adic Kummer–Leopoldt constant: Normalized p-adic regulator ⋮ \(p\)-rational fields, \(p\)-regular fields and restricted ramification ⋮ Topological models for stable motivic invariants of regular number rings ⋮ On the structure of the Galois group of the abelian closure of a number field

Cites Work

• \(\ell\)-classes infinitésimales d'un corps de nombres algébriques
• K-théorie des anneaux d'entiers de corps de nombres et cohomologie etale
• Relations between \(K_2\) and Galois cohomology
• Moore's theorem on uniqueness of reciprocity laws
• A finiteness theorem for K\(_2\) of a number field
• On the 2-primary part of a conjecture of Birch and Tate
• Groupe de Galois de la p-extension abélienne p-ramifiée maximale d'un corps de nombres.
• On Sylow 2-subgroups of K2OF for quadratic number fields F.
• Logarthme p-adique et groupes de Galois.
• Higher algebraic K-theory: I
• Critère de parité du nombre de classes des extensions abéliennes réelles de $Q$ de degré impair
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Remarks on \(K_ 2\) of number fields