Carlson, J.F. Acta Math Sinica (1999) 15: 81. doi:10.1007/s10114-999-0061-9

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.

Keywords

Group CohomologySupport varietiesCohomological varietiesAnnihilators of cohomology