Non-commutative Fitting invariants and annihilation of class groups

DOI10.1016/j.jalgebra.2010.02.039zbMath1222.11132OpenAlexW1978276013MaRDI QIDQ975087

Andreas Nickel

Publication date: 8 June 2010

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2010.02.039

zbMATH Keywords

class groupsequivariant \(L\)-valuesFitting invariant

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42) Orders in separable algebras (16H10)

Related Items (21)

On non-abelian higher special elements of \(p\)-adic representations ⋮ Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture ⋮ On derivatives of \(p\)-adic \(L\)-series at \(s = 0\) ⋮ Annihilation of Selmer groups for monomial CM-extensions ⋮ On Mordell-Weil groups and congruences between derivatives of twisted Hasse-Weil \(L\)-functions ⋮ On non-abelian Stark-type conjectures ⋮ On derivatives of Artin \(L\)-series ⋮ Congruences for critical values of higher derivatives of twisted Hasse–Weil $L$-functions, II ⋮ On Geometric Iwasawa Theory and Special Values of Zeta Functions ⋮ Fitting ideals in number theory and arithmetic ⋮ Leading terms of Artin L-series at negative integers and annihilation of higher K-groups ⋮ Integrality of Stickelberger elements attached to unramified extensions of imaginary quadratic fields ⋮ On the equivariant Tamagawa number conjecture for Tate motives and unconditional annihilation results ⋮ Annihilating wild kernels ⋮ On the equivariant Tamagawa number conjecture in tame CM-extensions, II ⋮ Notes on noncommutative fitting invariants (with an appendix by Henri Johnston and Andreas Nickel) ⋮ Fitting invariants in equivariant Iwasawa theory ⋮ On the \(p\)-adic Beilinson conjecture and the equivariant Tamagawa number conjecture ⋮ On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture ⋮ On non-abelian Brumer and Brumer–Stark conjecture for monomial CM-extensions ⋮ Conjectures of Brumer, Gross and Stark

Cites Work

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• On the equivariant Tamagawa number conjecture in tame CM-extensions
• The Stark conjectures on Artin \(L\)-functions at \(s=0\). Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher.
• On refined Stark conjectures in the non-abelian case
• Fitting ideals of class groups of real fields with prime power conductor
• Computing Fitting ideals of Iwasawa modules
• Toward equivariant Iwasawa theory. II.
• A non-abelian Stickelberger theorem
• A Local Approach to Chinburg's Root Number Conjecture
• Determining Fitting ideals of minus class groups via the equivariant Tamagawa number conjecture
• Rank Element of a Projective Module
• The Cohomology Groups of Tori in Finite Galois Extensions of Number Fields
• Algebraic \(K\)-theory
• Tamagawa numbers for motives with (non-commutative) coefficients

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