Varieties for cohomology with twisted coefficients |
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Authors: | Jon F. Carlson |
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Affiliation: | (1) Department of Mathematics, University of Georgia, 30602 Athens, GA, USA |
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Abstract: | Let G be a finite group and k a field of characteristic p > 0. In this paper we consider the support variety for the cohomology module Ext kG * (M, N) where M and N are kG-modules. It is the subvariety of the maximal ideal spectrum of H*(G, k) of the annihilator of the cohomology module. For modules in the principal block we show that that the variety is contained in the intersections of the varieties of M and N and the difference between the that intersection and the support variety of the cohomology module is contained in the group theoretic nucleus. For other blocks a new nucleus is defined and a similar theorem is proven. However in the case of modules in a nonprincipal block several new difficulties are highlighted by some examples. Partially supported by grants from NSF and EPSRC |
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Keywords: | Group Cohomology Support varieties Cohomological varieties Annihilators of cohomology |
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