无常变的布劳尔群的 p 主扭转的有界性

IF 1.3 1区 数学 Q1 MATHEMATICS Compositio Mathematica Pub Date : 2024-01-05 DOI:10.1112/s0010437x23007558
Marco D'Addezio
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引用次数: 0

摘要

我们证明了在特征 $p>0$ 的有限生成域上的无常变种的超越布劳尔群的 $p^\infty$-torsion 是有界的。这回答了斯科罗博加托夫(Skorobogatov)和扎尔欣(Zarhin)提出的一个关于无性变项的(变种)问题。为此,我们证明了除数的 "平泰特猜想"。我们还研究了布劳尔群中不在超越布劳尔群中的其他几何伽罗瓦不变$p^\infty$扭转类。与我们的主定理相反,这些类可以无限 $p$ 可分。我们解释了这些 $p$ 不可分塔的存在如何自然地与特征 $p$ 内伦-塞维里群的特殊化态射的失败相关联。
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Boundedness of the p-primary torsion of the Brauer group of an abelian variety

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. 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 $p$.

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来源期刊
Compositio Mathematica
Compositio Mathematica 数学-数学
CiteScore
2.10
自引率
0.00%
发文量
62
审稿时长
6-12 weeks
期刊介绍: Compositio Mathematica is a prestigious, well-established journal publishing first-class research papers that traditionally focus on the mainstream of pure mathematics. Compositio Mathematica has a broad scope which includes the fields of algebra, number theory, topology, algebraic and differential geometry and global analysis. Papers on other topics are welcome if they are of broad interest. All contributions are required to meet high standards of quality and originality. The Journal has an international editorial board reflected in the journal content.
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