Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21930
Brodmann, M; Hellus, M (2002). Cohomological patterns of coherent sheaves over projective schemes. Journal of Pure and Applied Algebra, 172(2-3):165-182.
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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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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Uncontrolled Keywords:||cohomology module; vanishing theorem; cohomological pattern|
|Deposited On:||27 May 2010 13:35|
|Last Modified:||23 Nov 2012 15:11|
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