Euler systems for Rankin--Selberg convolutions of modular forms

Abstract

We construct an Euler system in the cohomology of the tensor product of the Galois representations attached to two modular forms, using elements in the higher Chow groups of products of modular curves. We use this Euler system to prove a finiteness theorem for the strict Selmer group of the Galois representation when the associated p-adic Rankin--Selberg L-function is non-vanishing at s = 1.

Revised version with many updates and corrections

References in corpus (3)

• Iwasawa theory and p-adic L-functions over ${\mathbf{Z}}_p^2$-extensions
• Wach modules and critical slope p-adic L-functions
• A p-adic regulator map and finiteness results for arithmetic schemes

Cited by in corpus (31)

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• Rankin--Eisenstein classes in Coleman families
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• Images of adelic Galois representations for modular forms
• Higher Hida theory and p-adic L-functions for GSp(4)
• Euler systems for Hilbert modular surfaces
• Euler systems for modular forms over imaginary quadratic fields
• Iwasawa theory for Rankin--Selberg products of $p$-non-ordinary eigenforms
• Iwasawa theory for the symmetric square of a modular form
• Spherical varieties and norm relations in Iwasawa theory
• A higher rank Euler system for the multiplicative group over a totally real field
• P-adic L-functions in universal deformation families
• Regulators for Rankin-Selberg products of modular forms
• Euler systems with local conditions
• Rank--two Euler systems for symmetric squares
• P-adic Asai L-functions of Bianchi modular forms
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• On extra-zeros of p-adic Rankin-Selberg L-functions
• A class number formula for Picard modular surfaces
• Algebraicity of $L$-values for ${\text{GSp}}_4\times {\text{GL}}_2$ and ${\text{GSp}}_4\times {\text{GL}}_2\times {\text{GL}}_2$
• An introduction to $p$-adic $L$-functions
• Poles of p-adic Asai L-functions and distinguished representations
• The Spin $L$-function on ${\mathrm{GSp}}_6$ via a non-unique model
• On the factorisation of the $p$-adic Rankin-Selberg $L$-function in the supersingular case
• An Euler system for characters over an imaginary biquadratic field
• Explicit Cocycle of the Dedekind-Rademacher Cohomology Class and the Darmon-Dasgupta Measures
• Bounding Selmer groups for the Rankin--Selberg convolution of Coleman families
• P-adic Rankin-Selberg L-functions in universal deformation families and functional equations
• Control Theorems for Hilbert Modular Varieties