Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Monday, 12 January 2009, 14:00–15:00, Sn403

Christian González-Avilés: On Neron class groups and Tate-Shafarevich groups of abelian varieties

Abstract:

A classical exact sequence which defines the ideal class group of a number field may be extended to arbitrary tori (the classical case being that of the trivial torus G_m). This exact sequence for tori has an analog for abelian varieties, which leads to the definition of the Neron class group of an abelian variety A. In this talk I will show the connections that there exist between this class group and the better-known Tate-Shafarevich group of A. I will try to explain (or at least suggest) applications to the BSD conjecture.