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A rigidity result for highest order local cohomology modules
Authors:M Brodmann
Institution:1.Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland,? e-mail: brodmann@math.unizh.ch,CH
Abstract:Let M be a finitely generated faithful module over a noetherian ring R of dimension d < ¥ \infty and let \mathfrak a \subseteqq R {\mathfrak a} \subseteqq R be an ideal. We describe the (finite) set SuppR(H\mathfrak ad (M)) = AssR(H\mathfrak ad (M)) \textrm{Supp}_R(H_{\mathfrak a}^d (M)) = \textrm{Ass}_R(H_{\mathfrak a}^d (M)) of primes associated to the highest local cohomology module H\mathfrak ad (M) H_{\mathfrak a}^d (M) in terms of the local formal behaviour of \mathfrak a {\mathfrak a} . If R is integral and of finite type over a field, SuppR(H\mathfrak ad (M)) \textrm{Supp}_R(H_{\mathfrak a}^d (M)) is the set of those closed points of X = Spec(R) whose fibre under the normalization morphism n: X¢? X \nu : X' \rightarrow X contains points which are isolated in n-1(Spec(R/\mathfrak a)) \nu^{-1}(\textrm{Spec}(R/{\mathfrak a})) .
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