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arXiv · 1506.06703

Rankin--Eisenstein classes in Coleman families

David Loeffler·Sarah Livia Zerbes
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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.

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David Loeffler, Sarah Livia Zerbes. 2016-06-02. Rankin--Eisenstein classes in Coleman families. https://doi.org/10.1186/s40687-016-0077-6

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