论文标题
关于几何brauer群和泰特·沙法尔（Tate-Shafarevich）组
On geometric Brauer groups and Tate-Shafarevich groups
论文作者
论文摘要
让$ x $成为有限生成的特征性$ k $ p> 0 $的平稳的投射品种。我们证明了$ \ ell $ - 主要部分的$ \ mathrm {br}（x_ {k^s}）^{g_k} $的$ \ ell \ ell \ ell \ neq p $将暗示$ \ mathrm的prime-to-to-p $ part $ \ mathrm} $ { Tate和Lichtebaum定理，用于有限领域的品种。对于Abelian品种$ a $ a $ a $ a $ a $ k $，我们证明了$ a $ a $ $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $。
Let $X$ be a smooth projective variety over a finitely generated field $K$ of characteristic $p>0$. We proved that the finiteness of the $\ell$-primary part of $\mathrm{Br}(X_{K^s})^{G_K}$ for a single prime $\ell\neq p$ will imply the finiteness of the prime-to-$p$ part of $\mathrm{Br}(X_{K^s})^{G_K}$, generalizing a theorem of Tate and Lichtenbaum for varieties over finite fields. For an abelian variety $A$ over $K$, we proved a similar result for the Tate-Shafarevich group of $A$, generalizing a theorem of Schneider for abelian varieties over global function fields.
