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arXiv · 0811.2917

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

Peter Jossen
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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.

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Peter Jossen. 2011-10-24. On the second Tate-Shafarevich group of a 1-motive. https://doi.org/10.2140/ant.2013.7.2511

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