Local Galois Symbols on E x E
Number Theory
2009-07-03 v2 Algebraic Geometry
Abstract
This article is the first part of a two-part work on the Albanese kernel T_F(E x E), for an elliptic curve E over F. The main result furnishes information, for any odd prime p, about the kernel and image of the Galois symbol map from T_F(E \times E)/p to the Galois cohomology group H^2(F, E[p] (x) E[p]), for F a p-adic field and E/F ordinary, without requiring that the p-torsion points are F-rational. A key step is to show that the image is zero when the Galois module E[p] is non-semisimple. The forthcoming second part will deal with global questions.
Keywords
Cite
@article{arxiv.0808.1129,
title = {Local Galois Symbols on E x E},
author = {Jacob Murre and Dinakar Ramakrishnan},
journal= {arXiv preprint arXiv:0808.1129},
year = {2009}
}
Comments
A few small errors have been fixed. The main result is the same as before; in Motives and Algebraic Cycles: A Celebration in honour of Spencer J. Bloch, Filds Institute Proceedngs, AMS (2009)