On Neron class groups of abelian varieties

2009/09/25 by Gonzalez-Aviles, Cristian D.
#11G35 #14G25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0909.4803

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.

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