论文标题
在有限田地上，泰特·沙法雷维奇（Tate-Shafarevich
On the $p$-torsion of the Tate-Shafarevich group of abelian varieties over higher dimensional bases over finite fields
论文作者
论文摘要
我们证明了在有限领域的整体适当品种上，第一个有限扁平组方案的第一个扁平共同体学组是有限定理。结果，我们可以证明泰特·夏法尔（Tate-Shafarevich）小组的Abelian方案的有限态度不变性，而在$ p $ -part的ISEGENIES和此类基础上的变化下，我们的较高维基碱基的不变性。一路上，在这种情况下，我们将先前的结果推广到了Tate-Shafarevich组。
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.
