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Cohomological patterns of coherent sheaves over projective schemes


Brodmann, Markus; Hellus, Michael (2002). Cohomological patterns of coherent sheaves over projective schemes. Journal of Pure and Applied Algebra, 172(2-3):165-182.

Abstract

We study the sets P(X, ℱ) = (i,n) ∈ ℕ0 × ℤ Hi(X, ℱ(n)) ≠0}, where X is a projective scheme over a noetherian ring R0 and where ℱ is a coherent sheaf of OX-modules. In particular we show that P(X, ℱ) is a so called tame combinatorial pattern if the base ring R0 is semilocal and of dimension ≤ 1. If X = ℙR0d is a projective space over such a base ring R0, the possible sets P(X, ℱ) are shown to be precisely all tame combinatorial patterns of width ≤ d. We also discuss the "tameness problem" for arbitrary noetherian base rings R0 and prove some stability results for the R0-associated primes of the R0-modules Hi(X, ℱ (n)). © 2001 Elsevier Science B.V. All rights reserved.

Abstract

We study the sets P(X, ℱ) = (i,n) ∈ ℕ0 × ℤ Hi(X, ℱ(n)) ≠0}, where X is a projective scheme over a noetherian ring R0 and where ℱ is a coherent sheaf of OX-modules. In particular we show that P(X, ℱ) is a so called tame combinatorial pattern if the base ring R0 is semilocal and of dimension ≤ 1. If X = ℙR0d is a projective space over such a base ring R0, the possible sets P(X, ℱ) are shown to be precisely all tame combinatorial patterns of width ≤ d. We also discuss the "tameness problem" for arbitrary noetherian base rings R0 and prove some stability results for the R0-associated primes of the R0-modules Hi(X, ℱ (n)). © 2001 Elsevier Science B.V. All rights reserved.

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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
Scopus Subject Areas:Physical Sciences > Algebra and Number Theory
Uncontrolled Keywords:cohomology module, vanishing theorem, cohomological pattern
Language:English
Date:2002
Deposited On:27 May 2010 13:35
Last Modified:03 May 2024 01:38
Publisher:Elsevier
ISSN:0022-4049
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1016/S0022-4049(01)00144-X
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1906872
  • Content: Accepted Version
  • Language: English
  • Description: Preprint
  • Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)