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arXiv · 1503.02888

Rankin--Eisenstein classes and explicit reciprocity laws

Guido Kings·David Loeffler·Sarah Livia Zerbes
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Abstract

We construct three-variable $p$-adic families of Galois cohomology classes attached to Rankin convolutions of modular forms, and prove an explicit reciprocity law relating these classes to critical values of L-functions. As a consequence, we prove finiteness results for the Selmer group of an elliptic curve twisted by a 2-dimensional odd irreducible Artin representation when the associated $L$-value does not vanish.

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Guido Kings, David Loeffler, Sarah Livia Zerbes. 2015-03-10. Rankin--Eisenstein classes and explicit reciprocity laws. https://doi.org/10.4310/cjm.2017.v5.n1.a1

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