Acta Mathematica Sinica

, Volume 15, Issue 1, pp 81–92 | Cite as

Varieties for cohomology with twisted coefficients

  • Jon F. Carlson
Article

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 ExtkG*(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.

Keywords

Group Cohomology Support varieties Cohomological varieties Annihilators of cohomology 

1991MR Subject Classification

20C20 20C06 

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Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Jon F. Carlson
    • 1
  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA

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