On Neron class groups of abelian varieties

Details On Neron class groups of abelian varieties On Neron class groups of abelian varieties

2009-09-25

arxiv.org/abs/0909.4803v4

Mathematics

Number Theory

This is the final version of the paper accepted for publication

Scientific paper

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.

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