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Geometric domains with specified pseudo-dimensions


Brodmann, M; Sharp, R (2003). Geometric domains with specified pseudo-dimensions. Journal of Pure and Applied Algebra, 182(2-3):151-164.

Abstract

This paper pursues the study of the pseudo-supports of a finitely generated module over a finite-dimensional commutative Noetherian ring, and is particularly concerned with the properties of the pseudo-supports of a geometric normal local domain. It is shown that these pseudo-supports have certain properties that can be summarized by the so-called occurrence diagram of the ring, which is a certain subset of N0×N0. Standard properties of local cohomology modules enable one to conclude that there are obvious restrictions on the type of subset of N0×N0 that can be an occurrence diagram in this way, and much of the paper is devoted to consideration of whether a subset of N0×N0 that meets those obvious restrictions is an occurrence diagram of some geometric normal local domain. These occurrence diagrams are also used to assist with the production of examples that show that a question raised by C. Huneke, about certain sets related to Grothendieck's Finiteness Theorem for local cohomology, has a negative answer. © 2003 Elsevier Science B.V. All rights reserved.

Abstract

This paper pursues the study of the pseudo-supports of a finitely generated module over a finite-dimensional commutative Noetherian ring, and is particularly concerned with the properties of the pseudo-supports of a geometric normal local domain. It is shown that these pseudo-supports have certain properties that can be summarized by the so-called occurrence diagram of the ring, which is a certain subset of N0×N0. Standard properties of local cohomology modules enable one to conclude that there are obvious restrictions on the type of subset of N0×N0 that can be an occurrence diagram in this way, and much of the paper is devoted to consideration of whether a subset of N0×N0 that meets those obvious restrictions is an occurrence diagram of some geometric normal local domain. These occurrence diagrams are also used to assist with the production of examples that show that a question raised by C. Huneke, about certain sets related to Grothendieck's Finiteness Theorem for local cohomology, has a negative answer. © 2003 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
Uncontrolled Keywords:catenary local domain; finitely generated module; finite dimensional commutative Noetherian ring; occurrence diagram
Language:English
Date:2003
Deposited On:27 May 2010 13:25
Last Modified:05 Apr 2016 13:25
Publisher:Elsevier
ISSN:0022-4049
Publisher DOI:https://doi.org/10.1016/S0022-4049(03)00011-2
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1062.13001

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