On the second Tate-Shafarevich group of a 1-motive
Algebraic Geometry
2016-01-20 v3 Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0811.2917,
title = {On the second Tate-Shafarevich group of a 1-motive},
author = {Peter Jossen},
journal= {arXiv preprint arXiv:0811.2917},
year = {2016}
}
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28 pages