Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21933
Brodmann, M; Sharp, R (2002). On the dimension and multiplicity of local cohomology modules. Nagoya Mathematical Journal, 167:217-233.
This paper is concerned with a finitely generated module $M$ over a(commutative Noetherian) local ring $R$. In the case when $R$ is a homomorphic image of a Gorenstein local ring, one can use the well-known associativity formula for multiplicities, together with local duality and Matlis duality, to produce analogous associativity formulae for the local cohomology modules of $M$ with respect to the maximal ideal. The main purpose of this paper is to show that these formulae also hold in the case when $R$ is universally catenary and such that all its formal fibres are Cohen-Macaulay. These formulae involve certain subsets of the spectrum of $R$ called the pseudo-supports of $M$; these pseudo-supports are closed in the Zariski topology when $R$ is universally catenary and has the property that all its formal fibres are Cohen-Macaulay. However, examples are provided to show that, in general, these pseudo-supports need not be closed. We are able to conclude that the above-mentioned associativity formulae for local cohomology modules do not hold over all local rings.
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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:||Artinian module; multiplicity of local cohomology module; Cohen-Macaulay fibers; universally catenary module; Matlis dual; Noetherian local ring|
|Deposited On:||27 May 2010 16:08|
|Last Modified:||27 Nov 2013 19:00|
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