Rankin--Eisenstein classes for modular forms

Abstract

In this paper we make a systematic study of certain motivic cohomology classes ("Rankin-Eisenstein classes") attached to the Rankin--Selberg convolution of two modular forms of weight $\ge 2$. The main result is the computation of the $p$-adic syntomic regulators of these classes. As a consequence we prove many cases of the Perrin-Riou conjecture for Rankin--Selberg convolutions of cusp forms.

Updated version with minor corrections. To appear in Amer. J. Math

References in corpus (5)

• Rankin--Eisenstein classes and explicit reciprocity laws
• Rankin-Selberg Euler systems and p-adic interpolation
• Triple product p-adic L-functions associated to finite slope p-adic families of modular forms, with an appendix by Eric Urban
• Syntomic regulators of Asai--Flach classes
• Regulators for Rankin-Selberg products of modular forms

Cited by in corpus (20)

• Rankin--Eisenstein classes and explicit reciprocity laws
• Euler systems for GSp(4)
• Euler systems for Hilbert modular surfaces
• Iwasawa theory for Rankin--Selberg products of $p$-non-ordinary eigenforms
• Iwasawa theory for the symmetric square of a modular form
• Heegner points in Coleman families
• Syntomic regulators of Asai--Flach classes
• Rank--two Euler systems for symmetric squares
• P-adic Asai L-functions of Bianchi modular forms
• $p$-adic heights of Heegner points and Beilinson-Flach elements
• Anticyclotomic p-ordinary Iwasawa Theory of Elliptic Modular Forms
• P-adic L-functions and diagonal cycles for GSp(4) x GL(2) x GL(2)
• On p-adic regulators for GSp(4) x GL(2) and GSp(4) x GL(2) x GL(2)
• Iwasawa theory of twists of elliptic modular forms over imaginary quadratic fields at inert primes
• Eisenstein degeneration of Euler systems
• Algebraicity of $L$-values for ${\text{GSp}}_4\times {\text{GL}}_2$ and ${\text{GSp}}_4\times {\text{GL}}_2\times {\text{GL}}_2$
• A generalization of the Ross symbols in higher K-groups and hypergeometric functions I
• P-adic L-functions for GL(3)
• A universal Euler system for GSp(4)
• Iwasawa theory of automorphic representations of ${\mathrm{GL}}_{2n}$ at non-ordinary primes