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A rigidity result for highest order local cohomology modules


Brodmann, M (2002). A rigidity result for highest order local cohomology modules. Archiv der Mathematik, 79(2):87-92.

Abstract

Let M be a finitely generated faithful module over a noetherian ring R of dimension d < ¥ and let \mathfrak a \subseteqq R be an ideal. We describe the (finite) set SuppR(H\mathfrak ad (M)) = AssR(H\mathfrak ad (M)) of primes associated to the highest local cohomology module H\mathfrak ad (M) in terms of the local formal behaviour of \mathfrak a . If R is integral and of finite type over a field, SuppR(H\mathfrak ad (M)) is the set of those closed points of X = Spec(R) whose fibre under the normalization morphism n: X¢® X contains points which are isolated in n-1(Spec(R/\mathfrak a)).

Let M be a finitely generated faithful module over a noetherian ring R of dimension d < ¥ and let \mathfrak a \subseteqq R be an ideal. We describe the (finite) set SuppR(H\mathfrak ad (M)) = AssR(H\mathfrak ad (M)) of primes associated to the highest local cohomology module H\mathfrak ad (M) in terms of the local formal behaviour of \mathfrak a . If R is integral and of finite type over a field, SuppR(H\mathfrak ad (M)) is the set of those closed points of X = Spec(R) whose fibre under the normalization morphism n: X¢® X contains points which are isolated in n-1(Spec(R/\mathfrak a)).

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2 citations in Web of Science®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2002
Deposited On:27 May 2010 13:30
Last Modified:05 Apr 2016 13:25
Publisher:Springer
ISSN:0003-889X
Publisher DOI:10.1007/s00013-002-8289-y
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1925374
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1090.13011

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