Let $q$ be a non-negative integer. We prove that perfect field $K$ has cohomological dimension at most $q+1$ if, and only for any finite extension $L$ of homogeneous space $Z$ under smooth linear connected algebraic group over $L$, the $q$-th Milnor $K$-theory is spanned by images norms coming from extensions which rational point. also variant this result imperfect fields.

Let Γ \D be an arithmetic quotient of a symmetric space of non-compact type. A spine D0 is a Γ -equivariant deformation retraction of D with dimension equal to the virtual cohomological dimension of Γ . We explicitly construct a spine for the case of Γ = SU(2,1;Z[i]). The spine is then used to compute the cohomology of Γ \D with various local coefficients. © 2007 Elsevier Inc. All rights reserv...

In this paper we study compacta Y that are resolvable by a free p-adic action on compactum of lower dimension and focus whose cohomological with respect to the group Z[1/p] is 1.

A group has homological dimension ≤ 1 if it is locally free. We prove the converse provided that G satisfies the Atiyah Conjecture about L -Betti numbers. We also show that a finitely generated elementary amenable group G of cohomological dimension ≤ 2 possesses a finite 2dimensional model for BG and in particular that G is finitely presented and the trivial ZG-module Z has a 2-dimensional reso...

Using cohomological methods we discuss several issues related to chiral anomalies in noncommutative U(N) YM theories in any even dimension. We show that for each dimension there is only one solution of the WZ consistency condition and that there cannot be any reducible anomaly, nor any mixed anomaly when the gauge group is a product group. We also clarify some puzzling aspects of the issue of t...

We establish some sufficient conditions for the profinite and prop completions of an abstract group G of type FPm (resp of finite cohomological dimension, of finite Euler characteristics) to be of type FPm over the field Fp for a fixed natural prime p (resp. of finite cohomological p-dimension, of finite Euler p-characteristics). We apply our methods for orientable Poincaré duality groups G of ...

In this paper, we show that the CR $Q$-curvature is orthogonal to space of pluriharmonic functions on any closed strictly pseudoconvex manifold dimension at least five. To end, obtain a cohomological expression integral product and function.

The goal of this paper is to study the action groups on Zassenhaus and lower central filtrations finitely generated pro-p groups. We shall focus semisimple case. Particular attention given presented cohomological dimension less than or equal two.