Derived p-adic heights and p-adic L-functions
Number Theory
2012-02-29 v1
Abstract
If E is an elliptic curve defined over a number field and p is a prime of good ordinary reduction for E, a theorem of Rubin relates the p-adic height pairing on the p-power Selmer group of E to the first derivative of a cohomologically defined p-adic L-function attached to E. Bertolini and Darmon have defined a sequence of "derived" p-adic heights. In this paper we give an alternative definition of the p-adic height pairing and prove a generalization of Rubin's result, relating the derived heights to higher derivatives of p-adic L-functions. We also relate degeneracies in the derived heights to the failure of the Selmer group of E over a Z_p-extension to be "semi-simple" as an Iwasawa module, generalizing results of Perrin-Riou.
Cite
@article{arxiv.1202.6343,
title = {Derived p-adic heights and p-adic L-functions},
author = {Benjamin Howard},
journal= {arXiv preprint arXiv:1202.6343},
year = {2012}
}