On the Coates-Sinnott Conjecture

DOI10.1002/mana.200810802zbMath1187.11042OpenAlexW2147719279WikidataQ123337400 ScholiaQ123337400MaRDI QIDQ3643553

Cristian D. Popescu

Publication date: 9 November 2009

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200810802

zbMATH Keywords

annihilatorsK-groupsFitting ideals, Main conjecture

Mathematics Subject Classification ID

Zeta functions and (L)-functions of number fields (11R42) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33) (K)-theory of global fields (11R70) Galois cohomology (11R34)

Related Items (12)

An equivariant main conjecture in Iwasawa theory without the assumption \(\mu = 0\) ⋮ An Equivariant Main Conjecture in Iwasawa theory and applications ⋮ Fitting ideals of isotypic parts of even K-groups ⋮ Higher Stickelberger ideals and even 𝐾-groups ⋮ The Stickelberger splitting map and Euler systems in the \(K\)-theory of number fields ⋮ Divisibility properties of values of partial zeta functions at non-positive integers ⋮ The p-adic Coates–Sinnott Conjecture over maximal orders ⋮ Leading terms of Artin L-series at negative integers and annihilation of higher K-groups ⋮ Iwasawa main conjecture for the Carlitz cyclotomic extension and applications ⋮ Fitting invariants in equivariant Iwasawa theory ⋮ Fitting ideals of class groups in Carlitz-Hayes cyclotomic extensions ⋮ The Structure of Selmer Groups of Elliptic Curves and Modular Symbols

Cites Work

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• Class fields of abelian extensions of \(\mathbb Q\)
• Values of abelian \(L\)-functions at negative integers over totally real fields
• Algebraic \(K\)-theory of number fields and rings of integers and the Stickelberger ideal
• The structure of some minus class groups, and Chinburg's third conjecture for abelian fields
• Fitting ideals of class groups of real fields with prime power conductor
• Equivariant Weierstrass preparation and values of \(L\)-functions at negative integers
• An analogue of Stickelberger's theorem for the higher K-groups
• On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
• Some cases of Brumer's conjecture for abelian CM extensions of totally real fields
• The Iwasawa conjecture for totally real fields
• On a conjecture of Brumer
• Iwasawa theory and Fitting ideals

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