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

Autor:	Keller, Timo
Rok vydání:	2022
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry 14F20 (Primary) 11G10 14K15 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 14 pages, accepted for publication in Journal de Th\'eorie des Nombres de Bordeaux
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.05798 Zobrazit plný text záznamu View this record from Arxiv