Rankin--Eisenstein classes in Coleman families

Abstract

We show that the Euler system associated to Rankin--Selberg convolutions of modular forms, introduced in our earlier works with Lei and Kings, varies analytically as the modular forms vary in $p$-adic Coleman families. We prove an explicit reciprocity law for these families, and use this to prove cases of the Bloch--Kato conjecture for Rankin--Selberg convolutions.

Updated version, to appear in "Research in the Mathematical Sciences" (Robert Coleman memorial volume)

References in corpus (1)

• Images of adelic Galois representations for modular forms

Cited by in corpus (16)

• Iwasawa theory for Rankin--Selberg products of $p$-non-ordinary eigenforms
• Spherical varieties and norm relations in Iwasawa theory
• Heegner points in Coleman families
• Rank--two Euler systems for symmetric squares
• P-adic Asai L-functions of Bianchi modular forms
• Interpolation of Generalized Heegner Cycles in Coleman Families
• Interpolation of Beilinson-Kato elements and $p$-adic $L$-functions
• Functional Equation for p-adic Rankin-Selberg L-functions
• Perfectoid overconvergent Siegel modular forms and the overconvergent Eichler--Shimura morphism
• Eisenstein degeneration of Euler systems
• On the p-adic interpolation of unitary Friedberg--Jacquet periods
• P-adic L-functions for GL(3)
• Bounding Selmer groups for the Rankin--Selberg convolution of Coleman families
• p-adic interpolation of Gauss--Manin connections on nearly overconvergent modular forms and p-adic L-functions
• Arithmetic of critical $p$-adic $L$-functions
• P-adic Rankin-Selberg L-functions in universal deformation families and functional equations