An Equivariant Main Conjecture in Iwasawa theory and applications

DOI10.1090/jag/635zbMath1330.11070arXiv1103.3069OpenAlexW1812671821WikidataQ123016778 ScholiaQ123016778MaRDI QIDQ3192302

Cristian D. Popescu, Cornelius Greither

Publication date: 12 October 2015

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.3069

zbMATH Keywords

Brumer-Stark conjecture1-motivesequivariant main conjecture\(p\)-adic realizationsCoates-Sinnot conjecture

Mathematics Subject Classification ID

Iwasawa theory (11R23) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

Related Items (26)

Computing annihilators of class groups from derivatives of $L$-functions ⋮ The Eisenstein cocycle and Gross's tower of fields conjecture ⋮ An equivariant main conjecture in Iwasawa theory without the assumption \(\mu = 0\) ⋮ Abstract \(\ell\)-adic 1-motives and Tate's canonical class for number fields ⋮ On Iwasawa theory, zeta elements for \(\mathbb G_m\), and the equivariant Tamagawa number conjecture ⋮ Fitting ideals of isotypic parts of even K-groups ⋮ On derivatives of \(p\)-adic \(L\)-series at \(s = 0\) ⋮ Higher Stickelberger ideals and even 𝐾-groups ⋮ On the Brumer-Stark conjecture and refinements ⋮ The Eisenstein ideal for weight \(k\) and a Bloch-Kato conjecture for tame families ⋮ On the minus component of the equivariant Tamagawa number conjecture for \(\mathbb{G}_m\) ⋮ The p-adic Coates–Sinnott Conjecture over maximal orders ⋮ Integrality of Stickelberger elements attached to unramified extensions of imaginary quadratic fields ⋮ The second syzygy of the trivial \(G\)-module, and an equivariant main conjecture ⋮ Fitting invariants in equivariant Iwasawa theory ⋮ Equivariant Iwasawa theory for elliptic curves ⋮ On the \(p\)-adic Beilinson conjecture and the equivariant Tamagawa number conjecture ⋮ Fitting ideals of \(p\)-ramified Iwasawa modules over totally real fields ⋮ On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture ⋮ Non-commutative \(L\)-functions for \(p\)-adic representations over totally real fields ⋮ Picard 1-motives and Tate sequences for function fields ⋮ Notes on the dual of the ideal class groups of CM-fields ⋮ Conjectures of Brumer, Gross and Stark ⋮ On the Brumer-Stark conjecture ⋮ On Equivariant Characteristic Ideals of Real Classes ⋮ An equivariant Tamagawa number formula for Drinfeld modules and applications

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