整体F-正则簇的基本群概型
Fundamental group schemes of globally F-regular varieties
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中文总结 AI 辅助
该研究证明正特征代数闭域上连通正规整体F-正则射影簇的连通拟挠子覆盖塔稳定，其正则轨迹的Nori基本群概型有限且线性约化，有限性是Xu和Braun相关定理的正特征类比。
中文摘要 AI 辅助
我们证明：在特征为正的代数闭域上，连通正规整体F-正则射影簇的每一层连通拟挠子覆盖塔都会稳定；其正则轨迹的Nori基本群概型是有限且线性约化的。线性约化性表明任意拟挠子覆盖是驯服的，而有限性是Xu和Braun关于复射影Log Fano簇光滑轨迹基本群有限性定理的正特征类比。
英文摘要
We prove that every tower of connected quasi-torsor covers of a connected normal globally $F$-regular projective variety over an algebraically closed field of positive characteristic stabilizes, and that the Nori fundamental group scheme of its regular locus is finite and linearly reductive. The linear reductivity asserts that any quasi-torsor cover is tame, while the finiteness is a positive-characteristic analogue of theorems of Xu and Braun on the finiteness of the fundamental group of the smooth locus of a log Fano complex projective variety.
