  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.
