Diagonalisable $p$-groups cannot fix exactly one point on projective varieties

IF 0.9 1区 数学 Q2 MATHEMATICS
Olivier Haution
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引用次数: 2

Abstract

We prove an algebraic version of classical theorem in topology, asserting that an abelian p-group action on a smooth projective variety of positive dimension cannot fix exactly one point. When the group has only two elements, we prove that the number of fixed points cannot be odd. The main tool is a construction originally used by Rost in the context of the degree formula. The framework of diagonalisable groups allows us to include the case of base fields of characteristic p.
可对角化的p群不能在射影变体上精确地固定一个点
我们证明了经典拓扑学定理的一个代数版本,证明了正维光滑射影变化上的阿贝尔p群作用不能精确地固定一个点。当群只有两个元素时,我们证明了不动点的个数不能是奇数。主要工具是Rost最初在度公式中使用的结构。可对角群的框架允许我们考虑特征p的基域的情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.70
自引率
5.60%
发文量
23
审稿时长
>12 weeks
期刊介绍: The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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