On the depth of cohomology modules

Shank, R. James and Fleischmann, Peter and Kemper, Gregor (2004) On the depth of cohomology modules. Quarterly Journal of Mathematics, 55 (2). pp. 167-184. ISSN 0033-5606. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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We study the cohomology modules H-i(G,R) of a p-group G acting on a ring R of characteristic p, for i>0. In particular, we are interested in the Cohen-Macaulay property and the depth of H-i(G,R) regarded as an R-G-module. We first determine the support of H-i(G,R), which turns out to be independent of i. Then we study the Cohen-Macaulay property for H-1(G,R). Further results are restricted to the special case that G is cyclic and R is the symmetric algebra of a vector space on which G acts. We determine the depth of H-i(G,R) for i odd and obtain results in certain cases for i even. Along the way, we determine the degrees in which the transfer map Tr-G R -->R-G has non-zero image.

Item Type: Article
Uncontrolled keywords: INVARIANT RINGS
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:17
Last Modified: 19 May 2014 13:27
Resource URI: https://kar.kent.ac.uk/id/eprint/497 (The current URI for this page, for reference purposes)
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