相关论文: Compactly supported cohomology of buildings

We compute support of formal cohomology modules in a serial of non-trivial cases. Applications are given. For example, we compute injective dimension of certain local cohomology modules in terms of dimension of their's support.

This article uses homological methods for evaluating compactly supported cohomology groups of noncompact toric surfaces

Computations in the cohomology of finite groups.

The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the…

We present a construction of a compact connected space which supports a normal probability measure.

This article uses basic homological methods for evaluating examples of compactly supported cohomology groups of line bundles over projective curve.

As a part of our program for Geometric Arithmetic, we develop an arithmetic cohomology theory for number fields using theory of locally compact groups.

We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general complete metric spaces. Using this classification, we…

The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived…

We define a relative version of tiling cohomology for the purpose of comparing the topology of tiling spaces when one is a factor of the other. We illustrate this with examples, and outline a method for computing the cohomology of tiling…

The group of compactly supported homeomorphisms on a Tychonoff space can be topologized in a number of ways, including as a colimit of homeomorphism groups with a given compact support, or as a subgroup of the homeomorphism group of its…

We study properties of compactly supported $p$-adic pro-\'etale cohomology of smooth partially proper rigid analytic varieties. In particular, we prove a comparison theorem, in a stable range, with compactly supported syntomic cohomology,…

Leech's (co)homology groups of finite cyclic monoids are computed.

We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…

We study the Kac cohomology for matched pairs of locally compact groups. This cohomology theory arises from the extension theory of locally compact quantum groups. We prove a topological version of the Kac exact sequence and provide methods…

We prove that a compactly supported homeomorphism of a smooth manifold of dimension greater or equal to 5 can be approximated uniformly by compactly supported diffeomorphisms if and only if it is isotopic to a diffeomorphism. If the given…

We study cohomology for $p$-local finite groups with non-constant coefficient systems. In particular we show that under certain restrictions there exists a cohomology transfer map in this context, and deduce the standard consequences.

Under a certain condition A we give a construction to calculate the intersection cohomology of a rank one local system on the complement to a hyperplane-like divisor

We consider the union of certain irreducible components of cohomological support loci of the canonical bundle, which we call standard. We prove a structure theorem about them and single out some particular cases, recovering and improving…

We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…