On the Galois structure of algebraic integers and S-units

DOI10.1007/BF01394240zbMath0564.12016MaRDI QIDQ1057935

Ted Chinburg

Publication date: 1983

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

Full work available at URL: https://eudml.org/doc/143076

zbMATH Keywords

Gauss sumsregulatoralgebraic integersGalois module structureresolventsclass groupcanonical classTate conjectureArtin L-series\(Ext^ 2_ G\)Grothendieck group of group ringS-units

Mathematics Subject Classification ID

Grothendieck groups, (K)-theory, etc. (16E20) Zeta functions and (L)-functions of number fields (11R42) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

Related Items (23)

On the equivariant Tamagawa number conjecture for \(A_4\)-extensions of number fields ⋮ On the conjecture of Lichtenbaum and of Chinburg over function fields ⋮ Numerical Evidence for a Conjectural Generalization of Hilbert's Theorem 132 ⋮ Motivic \(L\)-functions and Galois module structures ⋮ On derivatives of \(p\)-adic \(L\)-series at \(s = 0\) ⋮ The strong Stark conjecture for totally odd characters ⋮ On non-abelian Stark-type conjectures ⋮ On derivatives of Artin \(L\)-series ⋮ On Geometric Iwasawa Theory and Special Values of Zeta Functions ⋮ On the p‐adic Stark conjecture at s=1 and applications ⋮ Values of \(L\)-functions at \(s = 0\) ⋮ THE EQUIVALENCE OF RUBIN'S CONJECTURE AND THE ETNC/LRNC FOR CERTAIN BIQUADRATIC EXTENSIONS ⋮ Congruences between derivatives of geometric \(L\)-functions. With an appendix by David Burns, King Fai Lai and Ki-Seng Tan ⋮ On the equivariant Tamagawa number conjecture in tame CM-extensions ⋮ Computation of Stark-Tamagawa units ⋮ On the equivariant Tamagawa number conjecture for Tate motives and unconditional annihilation results ⋮ On the equivariant Tamagawa number conjecture in tame CM-extensions, II ⋮ Galois structure ofS-units ⋮ Cyclotomic Galois module structure and the second Chinburg invariant ⋮ On the \(p\)-adic Beilinson conjecture and the equivariant Tamagawa number conjecture ⋮ Unnamed Item ⋮ Conjectures of Brumer, Gross and Stark ⋮ \(\mathcal S\)-units and \(\mathcal S\)-class groups of a cyclic number field of prime degree

Cites Work

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• Induced representations and projective modules
• Class fields of abelian extensions of \(\mathbb Q\)
• Classes d'idéaux des corps abéliens et nombres de Bernoulli généralisés
• Unités cyclotomiques, unités semi-locales et \(\mathbb{Z}_\ell\)-extensions
• On l-adic zeta functions
• K-theory of finite groups and orders. Notes by E. Graham Evans
• Values of \(L\)-functions at \(s=1\). I: \(L\)-functions for quadratic forms
• Periodic Projective Resolutions
• Onp-adicL-functions and cyclotomic fields. II
• Some Problems of Galois Module Structure for Wild Extensions
• The Cohomology Groups of Tori in Finite Galois Extensions of Number Fields

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