Multiplicative reduction and the cyclotomic main conjecture for \(\mathrm{GL}_2\)

DOI10.2140/pjm.2016.283.171zbMath1368.11060arXiv1407.1093OpenAlexW3103143554WikidataQ123011062 ScholiaQ123011062MaRDI QIDQ297544

Christopher M. Skinner

Publication date: 27 June 2016

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.1093

zbMATH Keywords

Iwasawa theorySelmer groupsspecial values of \(L\)-functions

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23)

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The Birch and Swinnerton-Dyer Conjecture: A brief survey ⋮ Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces ⋮ Deformations of Kolyvagin systems ⋮ On the indivisibility of derived Kato's Euler systems and the main conjecture for modular forms ⋮ Elliptic curves and Thompson's sporadic simple group ⋮ Zeta morphisms for rank two universal deformations ⋮ A \(p\)-adic Waldspurger formula and the conjecture of Birch and Swinnerton-Dyer ⋮ Elliptic curves over \(\mathbb{Q}_\infty\) are modular ⋮ Irreducibility of limits of Galois representations of Saito-Kurokawa type ⋮ Remarks on Kato's Euler systems for elliptic curves with additive reduction ⋮ Iwasawa theory for modular forms ⋮ Beilinson-Kato and Beilinson-Flach elements, Coleman-Rubin-Stark classes, Heegner points and a conjecture of Perrin-riou ⋮ From the Monster to Thompson to O’Nan ⋮ Chromatic Selmer groups and arithmetic invariants of elliptic curves ⋮ Elliptic curves with exceptionally large analytic order of the Tate–Shafarevich groups

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