Nilpotence of Frobenius action and the Hodge filtration on local cohomology

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• 作者：Vasudevan Srinivas^a ; ^{srinivas@math.tifr.res.in" class="auth_mail" title="E-mail the corresponding author} ; Shunsuke Takagi^b ; ^{stakagi@ms.u-tokyo.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：13A35 ; 13C20 ; 14C30 ; 14F22
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：10 January 2017
• 年：2017
• 卷：305
• 期：Complete
• 页码：456-478
• 全文大小：533 K

文摘

An F  -nilpotent local ring is a local ring class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870816312579&_mathId=si1.gif&_user=111111111&_pii=S0001870816312579&_rdoc=1&_issn=00018708&md5=efb05837f5ce9b05620d1ae1a89ea604" title="Click to view the MathML source">(R,m)class="mathContainer hidden">class="mathCode">$(R,\mathfrak{m})$ of prime characteristic defined by the nilpotence of the Frobenius action on its local cohomology modules class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870816312579&_mathId=si2.gif&_user=111111111&_pii=S0001870816312579&_rdoc=1&_issn=00018708&md5=58b84d8db984662717764ac164cf7ef6">class="imgLazyJSB inlineImage" height="17" width="50" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0001870816312579-si2.gif">class="mathContainer hidden">class="mathCode">$H_{\mathfrak{m}}^i(R)$. 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.