On torsors under abelian varieties

Details On torsors under abelian varieties On torsors under abelian varieties

2011-06-08

arxiv.org/abs/1106.1540v2

Mathematics

Algebraic Geometry

Scientific paper

Let A be an abelian variety over a local field K of mixed characteristic and with algebraically closed residue field. We provide a geometric construction (via the relative Picard functor) of the Shafarevich duality between the group of isomorphism classes of torsors under A and the "fundamental group" of the N\'eron model of the dual abelian variety A'. An analogous construction works over fields of positive characteristic p providing a duality on the prime-to-p parts.

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