We show that for certain discrete p-perfect groups G, in particular for all pperfect groups of finite cohomological dimension, the loop space on the p-completed classifying space ΩBGp is a retract of the loop spaces on a certain finite complex. For finite vcd groups we provide a bound on the the dimension of such a complex.

In this paper, considering the difference between the finiteness dimension and cohomological dimension for a finitely generated module, we investigate the asymptotic behavior of grades of components of graded local cohomology modules with respect to irrelevant ideal; as long as we study some artinian and tameness property of such modules.

In this paper we present algorithms that compute certain local cohomology modules associated to a ring of polynomials containing the rational numbers. In particular we are able to compute the local cohomological dimension of algebraic varieties in characteristic zero.