Rankin--Eisenstein classes in Coleman families
Number Theory
2018-02-15 v2
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 -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.
Keywords
Cite
@article{arxiv.1506.06703,
title = {Rankin--Eisenstein classes in Coleman families},
author = {David Loeffler and Sarah Livia Zerbes},
journal= {arXiv preprint arXiv:1506.06703},
year = {2018}
}
Comments
Updated version, to appear in "Research in the Mathematical Sciences" (Robert Coleman memorial volume)