English

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