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A cohomological stability result for projective schemes over surfaces


Brodmann, M (2007). A cohomological stability result for projective schemes over surfaces. Journal für die Reine und Angewandte Mathematik, 606:179-192.

Abstract

Let π : X → X0 be a projective morphism of schemes such that X0 is noetherian and essentially of finite type over a field K. Let i N0, let F be a coherent sheaf of -modules and let L be an ample invertible sheaf over X. We show that the set of associated points of the higher direct image sheaf ultimately becomes constant if n tends to −∞, provided X0 has dimensione 2. If , this stability result need not hold any more.

To prove this, we show that the set of associated primes of the n-th graded component of the i-th local cohomology module of a finitely generated graded module M over a homogeneous noetherian ring which is essentially of finite type over a field becomes ultimately constant in codimension 2 if n tends to −∞.

Let π : X → X0 be a projective morphism of schemes such that X0 is noetherian and essentially of finite type over a field K. Let i N0, let F be a coherent sheaf of -modules and let L be an ample invertible sheaf over X. We show that the set of associated points of the higher direct image sheaf ultimately becomes constant if n tends to −∞, provided X0 has dimensione 2. If , this stability result need not hold any more.

To prove this, we show that the set of associated primes of the n-th graded component of the i-th local cohomology module of a finitely generated graded module M over a homogeneous noetherian ring which is essentially of finite type over a field becomes ultimately constant in codimension 2 if n tends to −∞.

Citations

3 citations in Web of Science®
4 citations in Scopus®
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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:June 2007
Deposited On:10 Apr 2009 11:54
Last Modified:05 Apr 2016 13:12
Publisher:De Gruyter
ISSN:0075-4102
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1515/CRELLE.2007.040
Related URLs:http://www.math.uzh.ch/fileadmin/math/preprints/22-05.pdf (Author)

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