On the second Tate-Shafarevich group of a 1-motive

Details On the second Tate-Shafarevich group of a 1-motive On the second Tate-Shafarevich group of a 1-motive

2008-11-18

arxiv.org/abs/0811.2917v3

Mathematics

Algebraic Geometry

28 pages

Scientific paper

We prove finiteness results for Tate--Shafarevich groups in degree 2 associated with 1--motives, rely them to Leopoldt's conjecture, and present an example of a semiabelian variety with an infinite Tate--Shafarevich group in degree 2. We also establish an arithmetic duality theorem for 1--motives over number fields which complements earlier results of Harari and Szamuely in this direction.

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