Rankin--Eisenstein classes and explicit reciprocity laws
Number Theory
2023-11-23 v6
Abstract
We construct three-variable -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 -value does not vanish.
Cite
@article{arxiv.1503.02888,
title = {Rankin--Eisenstein classes and explicit reciprocity laws},
author = {Guido Kings and David Loeffler and Sarah Livia Zerbes},
journal= {arXiv preprint arXiv:1503.02888},
year = {2023}
}
Comments
Updated Nov 2023 to add a correction (included separately at the end of the file)