论文标题
$ p $ - 主要扭转Abelian品种的Brauer群
Boundedness of the $p$-primary torsion of the Brauer group of an abelian variety
论文作者
论文摘要
我们证明，在有限生成的特征$ p> 0 $的字段上，$ p^\ infty $ torsion是一个阿贝里安品种的$ p^\ infty $ torsion。这回答了Skorobogatov和Zarhin提出的Abelian品种的（A）问题的（A）问题。为此，我们证明了分区的“坦率猜想”。在文本中，我们还研究了不在先验的Brauer组中的Brauer群体的其他几何galois-invariant $ p^\ infty $ torsion类。与我们的主要定理相比，这些课程可以是无限$ p $ - 可分布的。我们解释了这些$ p $ - 可分布的塔的存在自然与néron的专业形态的溢流性失败 - 特征性$ p $。
We prove that the $p^\infty$-torsion of the transcendental Brauer group of an abelian variety over a finitely generated field of characteristic $p>0$ is bounded. This answers a (variant of a) question asked by Skorobogatov and Zarhin for abelian varieties. To do this, we prove a "flat Tate conjecture" for divisors. In the text, we also study other geometric Galois-invariant $p^\infty$-torsion classes of the Brauer group which are not in the transcendental Brauer group. These classes, in contrast with our main theorem, can be infinitely $p$-divisible. We explain how the existence of these $p$-divisible towers is naturally related to the failure of surjectivity of specialisation morphisms of Néron--Severi groups in characteristic $p$.
