On Neron class groups of abelian varieties
Number Theory
2010-10-01 v4 Algebraic Geometry
Abstract
Let F be a global field and let S denote a nonempty finite set of primes of F containing the set S' of archimedean primes of F. In this paper we study the Neron S-class group C_{A,F,S} of an abelian variety A defined over F. In the well-known analogy that exists between the Birch and Swinnerton-Dyer conjecture for A over F and Dirichlet's analytic class number formula for the field F (in the number field case), the finite group C_{A,F,S'} (not the Tate-Shafarevich group of A) is a natural analog of the ideal class group of F.
Cite
@article{arxiv.0909.4803,
title = {On Neron class groups of abelian varieties},
author = {Cristian D. Gonzalez-Aviles},
journal= {arXiv preprint arXiv:0909.4803},
year = {2010}
}
Comments
This is the final version of the paper accepted for publication