有限域上高维基上阿贝尔变体的Tate-Shafarevich群的p-扭转

IF 0.3 4区数学 Q4 MATHEMATICS

Journal De Theorie Des Nombres De Bordeaux Pub Date : 2022-03-11 DOI:10.5802/jtnb.1211

Timo Keller

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引用次数: 1

摘要

我们证明了有限域上积分正规本变种上的有限平坦群格式的第一平坦上同调群的一个有限性定理。因此，我们可以证明阿贝尔格式的Tate-Shafarevich群在高维基底上的有限性的不变性，以及p部分在这些基底上的变换。在此基础上，我们推广了以前在这种情况下关于Tate-Shafarevich群的结果。

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

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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来源期刊

Journal De Theorie Des Nombres De Bordeaux MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The Journal de Théorie des Nombres de Bordeaux publishes original papers on number theory and related topics (not published elsewhere).