2001/10/22 by Manuel Blickle, Blickle, Manuel
Mathematics · #13N10 #14B15 #14F43 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AC #math.AG #msc:13N10 #msc:14B15 #msc:14F43
paper · pdf · doi:10.48550/arxiv.math/0110244
University of Michigan Dissertation
arxiv created 2001/10/22 · openalex publication_date 2001/10/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a regular, local and F-finite ring defined over a field of finite characteristic. Let I be an ideal of height c with normal quotient A=R/I. It is shown that the local cohomology module HcI(R) contains a unique simple DR--submodule L(A,R). This should be viewed as a finite characteristic analog of the Kashiwara--Brylinski DR--module in characteristic zero which corresponds to the intersection cohomology complex via the Riemann--Hilbert correspondence. Besides the existence of L(A,R), more importantly, we give its construction as a certain dual of the tight closure of zero in Hdm(A). We obtain a precise DR--simplicity criterion for HcI(R), namely HcI(R) is DR--simple if and only if the tight closure of zero in Hdm(A) is Frobenius nilpotent, in particular this is the case if A is F--rational. Furthermore, the techniques developed imply a result in tight closure theory, saying that the parameter test module commutes with completion.