Euler systems for Rankin–Selberg convolutions of modular forms

Abstract

We construct a 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 these elements to prove a finiteness theorem for the strict Selmer group of the Galois representation when the associated $p$-adic Rankin–Selberg $L$-function is nonvanishing at $s = 1$.