Nilpotence of Frobenius action and the Hodge filtration on local cohomology
Nilpotence of Frobenius action and the Hodge filtration on local cohomology
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Frobenius 作用的幂零性和局部上同调的 Hodge 过滤
DOI：
10.1016/j.aim.2016.09.029
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发表时间：
2017
影响因子：
1.7
通讯作者：
Shunsuke Takagi
中科院分区：
文献类型：
--
作者：
Vasudevan Srinivas;Shunsuke Takagi
F-幂零局部环是由Frobenius作用在其局部上同调模Hmi（R）上的幂零性定义的具有素特征的局部环（R，m）。一个特征为零的奇点称为F-幂零型奇点，如果它的模p约化对几乎所有p都是F-幂零的.本文给出了F-幂零型三维正规孤立奇点的Hodge理论解释.在分次的情况下，这产生了一个表征这些奇异性的除数类群和布劳尔群。
An F-nilpotent local ring is a local ring (R, m) of prime characteristic defined by the nilpotence of the Frobenius action on its local cohomology modules H m i (R). A singularity in characteristic zero is said to be of F-nilpotent type if its modulo p reduction is F-nilpotent for almost all p. In this paper, we give a Hodge-theoretic interpretation of three-dimensional normal isolated singularities of F-nilpotent type. In the graded case, this yields a characterization of these singularities in terms of divisor class groups and Brauer groups.