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 $s = 1$.

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Authors

Antonio Lei

McGill University, Montreal, QC, Canada

Current address:

Université Laval, Québec, Canada David Loeffler

Mathematics Institute, University of Warwick, Coventry, UK

Sarah Livia Zerbes

University College London, London, UK