Euler systems for modular forms over imaginary quadratic fields

DOI10.1112/S0010437X14008033zbMath1376.11050arXiv1311.0175WikidataQ115288118 ScholiaQ115288118MaRDI QIDQ3447682

Sarah Livia Zerbes, David Loeffler, Antonio Lei

Publication date: 27 October 2015

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.0175

zbMATH Keywords

Selmer groupsEuler systemsGalois representationsRankin-Selberg convolution

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (p)-adic theory, local fields (11F85) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Modular and Shimura varieties (14G35)

Related Items (11)

On the growth of $\mu $-invariant in Iwasawa theory of supersingular elliptic curves ⋮ EULER SYSTEMS FOR HILBERT MODULAR SURFACES ⋮ Construction of anti-cyclotomic Euler systems of modular abelian varieties, and the ranks of their Mordell-Weil groups ⋮ An explicit comparison of anticyclotomic p-adic L-functions for Hida families ⋮ On the Iwasawa invariants of BDP Selmer groups and BDP \(p\)-adic \(L\)-functions ⋮ Iwasawa theory for the symmetric square of a modular form ⋮ Anticyclotomic \(p\)-ordinary Iwasawa theory of elliptic modular forms ⋮ Euler systems with local conditions ⋮ Beilinson-Kato and Beilinson-Flach elements, Coleman-Rubin-Stark classes, Heegner points and a conjecture of Perrin-riou ⋮ Iwasawa theory for \(\mathrm{GL}_2\times \mathrm{Res}_{K/\mathbb{Q}}\mathrm{GL}_1\) ⋮ Beilinson-Flach elements and Euler systems II: The Birch-Swinnerton-Dyer conjecture for Hasse-Weil-Artin 𝐿-series

Cites Work

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• Generalized Heegner cycles and \(p\)-adic Rankin \(L\)-series. With an appendix by Brian Conrad
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• Iwasawa theory and p-adic L-functions over ${\mathbb Z}_{p}^{2}$-extensions
• Diagonal cycles and Euler systems I: A $p$-adic Gross-Zagier formula
• Bipartite Euler systems
• on l-adic representations attached to modular forms II
• Fonctions L p -Adiques Associees a Une Forme Modulaire Et a Un Corps Quadratique Imaginaire
• Beilinson-Flach elements and Euler systems I: Syntomic regulators and 𝑝-adic Rankin 𝐿-series

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