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arXiv · 2203.05798

On the $p$-torsion of the Tate-Shafarevich group of abelian varieties over higher dimensional bases over finite fields

Timo Keller
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Abstract

We prove a finiteness theorem for the first flat cohomology group of finite flat group schemes over integral normal proper varieties over finite fields. As a consequence, we can prove the invariance of the finiteness of the Tate-Shafarevich group of Abelian schemes over higher dimensional bases under isogenies and alterations over/of such bases for the $p$-part. Along the way, we generalize previous results on the Tate-Shafarevich group in this situation.

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Timo Keller. 2022-03-11. On the $p$-torsion of the Tate-Shafarevich group of abelian varieties over higher dimensional bases over finite fields. https://arxiv.org/abs/2203.05798

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