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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 pp-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.Comment: Updated version, to appear in "Research in the Mathematical Sciences" (Robert Coleman memorial volume

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