Euler systems for Rankin-Selberg convolutions of modular forms

DOI10.4007/annals.2014.180.2.6zbMath1315.11044arXiv1212.4056OpenAlexW2102958515WikidataQ115288120 ScholiaQ115288120MaRDI QIDQ742912

David Loeffler, Sarah Livia Zerbes, Antonio Lei

Publication date: 19 September 2014

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.4056

zbMATH Keywords

modular formRankin-Selberg convolution\(p\)-adic \(L\)-functionEuler systemHida familySelmer groupBeilinson-Flach elements

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (p)-adic theory, local fields (11F85) Galois representations (11F80) (Equivariant) Chow groups and rings; motives (14C15)

Related Items (43)

Euler systems for \(\mathrm{GSp}(4)\) ⋮ The Iwasawa main conjectures for \(\operatorname{GL}_2\) and derivatives of \(p\)-adic \(L\)-functions ⋮ Euler systems for modular forms over imaginary quadratic fields ⋮ Factorization of \(p\)-adic Rankin \(L\)-series ⋮ Elliptic curves of rank two and generalised Kato classes ⋮ Regulators for Rankin-Selberg products of modular forms ⋮ EULER SYSTEMS FOR HILBERT MODULAR SURFACES ⋮ Rankin-Eisenstein classes in Coleman families ⋮ On analogues of Mazur-Tate type conjectures in the Rankin-Selberg setting ⋮ Construction of anti-cyclotomic Euler systems of modular abelian varieties, and the ranks of their Mordell-Weil groups ⋮ On the rank-part of the Mazur-Tate refined conjecture for higher weight modular forms ⋮ Iwasawa theory for Rankin-Selberg products of \(p\)-nonordinary eigenforms ⋮ Iwasawa main conjecture for Rankin-Selberg \(p\)-adic \(L\)-functions ⋮ Height one specializations of Selmer groups ⋮ Euler systems and the Bloch-Kato conjecture for automorphic Galois representations ⋮ On extra zeros of 𝑝-adic Rankin–Selberg 𝐿-functions ⋮ ON THE EXCEPTIONAL SPECIALIZATIONS OF BIG HEEGNER POINTS ⋮ Main conjectures for higher rank nearly ordinary families. I ⋮ On the Iwasawa invariants of BDP Selmer groups and BDP \(p\)-adic \(L\)-functions ⋮ Norm-compatible systems of Galois cohomology classes for \(\mathrm{GSp}_6\) ⋮ \(p\)-adic Asai \(L\)-functions of Bianchi modular forms ⋮ Diagonal cycles and Euler systems II: The Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin $L$-functions ⋮ A \(p\)-adic interpolation of generalized Heegner cycles and integral Perrin-Riou twist. I ⋮ P-adic L-functions in universal deformation families ⋮ IMAGES OF ADELIC GALOIS REPRESENTATIONS FOR MODULAR FORMS ⋮ On norm relations for Asai–Flach classes ⋮ Iwasawa theory for symmetric squares of non-\(p\)-ordinary eigenforms ⋮ Iwasawa theory for the symmetric square of a modular form ⋮ Beilinson-Flach elements, Stark units and \(p\)-adic iterated integrals ⋮ Anticyclotomic \(p\)-ordinary Iwasawa theory of elliptic modular forms ⋮ Derived Beilinson-Flach elements and the arithmetic of the adjoint of a modular form ⋮ Euler systems with local conditions ⋮ Norm-compatible systems of cohomology classes for GU(2,2) ⋮ The Conjecture of Birch and Swinnerton-Dyer ⋮ Higher Hida theory and \(p\)-adic \(L\)-functions for \(\mathrm{GSp}_4\) ⋮ Spherical varieties and norm relations in Iwasawa theory ⋮ Rank-two Euler systems for symmetric squares ⋮ Iwasawa theory for \(\mathrm{GL}_2\times \mathrm{Res}_{K/\mathbb{Q}}\mathrm{GL}_1\) ⋮ Bounding Selmer Groups for the Rankin–Selberg Convolution of Coleman Families ⋮ Beilinson-Flach elements and Euler systems I: Syntomic regulators and 𝑝-adic Rankin 𝐿-series ⋮ Iwasawa theory of automorphic representations of \(\mathrm{GL}_{2n}\) at non-ordinary primes ⋮ Beilinson-Flach elements and Euler systems II: The Birch-Swinnerton-Dyer conjecture for Hasse-Weil-Artin 𝐿-series ⋮ A higher rank Euler system for Gm over a totally real field

Uses Software

• SageMath

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