发表机构
Tsinghua University（清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为光滑超曲面的自同构群建立可提升性与F-可提升性的小子群判据，通过检验低阶p-子群即可判定，并给出最优界。
AI 中文摘要
本文在先前Sylow判据的基础上，建立了特征零代数闭域上光滑超曲面X的线性自同构群G的可提升性与F-可提升性的小子群判据。当dim X = p-2（p为奇素数）时，我们证明G的任意有限子群的（F-）可提升性可通过其阶至多p^2的p-子群来检验。当X为维数2p-2的p次超曲面时，我们证明G的（F-）可提升性可通过其所有阶至多p^3的p-子群来检验，且该界对p≥5是精确的。当p=3时，该界改进为9，从而给出光滑三次四fold的相应判据。
英文摘要
In this paper, building on our previous Sylow criteria, we establish small-subgroup criteria of liftability and $F$-liftability for the linear automorphism group $G$ of smooth hypersurfaces $X$ over algebraically closed field of characteristic zero. When $\mathrm{dim} X = p-2$ for some odd prime $p$, we prove that ($F$-)liftability of any finite subgroup of $G$ can be tested on its $p$-subgroups of order at most $p^2$. When $X$ is a degree $p$ hypersurface of dimension $2p-2$, we prove that ($F$-)liftability of $G$ can be tested on all its $p$-subgroups of order at most $p^3$, which is sharp for $p\geq5$. When $p=3$, this bound improves to $9$, giving the corresponding criteria for smooth cubic fourfolds.
Comments21 pages. Comments welcome!
