The Cohomology Ring of a Finite Group

The Cohomology of a Coxeter Group with Group Ring Coefficients

Pure Injectives and the Spectrum of the Cohomology Ring of a Finite Group

Let G be a finite group and k be a field of characteristic p. The connection between the modular representations and the cohomology of G has been a subject of major interest over the last several years. For example, recent study of the stable category of kG-modules StMod(kG) led Rickard [27] to introduce certain idempotent modules and functors. This has led to a theory of varieties for infinite...

On the Second Cohomology Group of a Finite Group

We shall in fact prove it with C = 2. In the same situation, Aschbacher and Guralnick proved in Theorem A of [1] that \H\G, V)\<\V\. Guralnick has recently improved this bound to \H(G, V)\^\V\l, which is the best possible. At the present time, a proof of the intermediate result \H(G, V)\ «= |V|S is available in preprint form [13]. By using this result, it should be possible with a little extra ...

On Nilpotent ideals in the cohomology ring of a finite group

In this paper we find upper bounds for the nilpotency degree of some ideals in the cohomology ring of a finite group by studying fixed point free actions of the group on suitable spaces. The ideals we study are the kernels of restriction maps to certain collections of proper subgroups. We recover the Quillen-Venkov lemma and the Quillen F-injectivity theorem as corollaries, and discuss some gen...

The Coherent Cohomology Ring of an Algebraic Group

Let G be a group scheme of finite type over a field, and consider the cohomology ring H∗(G) with coefficients in the structure sheaf. We show that H∗(G) is a free module of finite rank over its component of degree 0, and is the exterior algebra of its component of degree 1. When G is connected, we determine the Hopf algebra structure of H∗(G).