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: | |
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: |