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<sub>kG</sub><sup>*</sup>（M,N） where M and N are kG-mod...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<sub>kG</sub><sup>*</sup>（M,N） where M and N are kG-modules.It is the subvariety of the maximal ideal spectrum of H<sup>*</sup>（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.展开更多
基金Partially supported by grants from NSF and EPSRC
文摘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<sub>kG</sub><sup>*</sup>（M,N） where M and N are kG-modules.It is the subvariety of the maximal ideal spectrum of H<sup>*</sup>（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.
