Related papers: A Note on Arithmetic Cohomologies for Number Field…

We develop a numerical approach to cohomology. Essentially, vector spaces and linear maps are replaced by real numbers, which represent dimensions of vector spaces and ranks of linear maps. We use this to refine ideas of Van der Geer and…

The purpose of this survey is to describe how locally compact groups can be studied as geometric objects. We will emphasize the main ideas and skip or just sketch most proofs, often referring the reader to our much more detailed book…

We compute the cohomology with group ring coefficients of the complement of a finite collection of affine hyperplanes in a finite dimensional complex vector space. It is nonzero in exactly one degree, namely the degree equal to the rank of…

Recently, the authors of this paper introduced logarithmic Hochschild (co)homology of logarithmic spaces in a geometric way using formality of derived intersections. In this paper, the authors extend the decomposition theorem for the…

In this article, we will define two canonical cohomology theories for Hopf $C^*$-algebras and for Hopf von Neumann algebras (with coefficients in their bicomodules). We will then study the situations when these cohomologies vanish. The…

We prove a duality result for the analytic cohomology of Lie groups over non-archimedean fields acting on locally convex vector spaces.

We survey old and new results about the cohomology of the moduli space $A_g$ of principally polarized abelian varieties of genus $g$ and its compactifications. The main emphasis lies on the computation of the cohomology for small genus and…

In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We develop the theory completely within the von Neumann algebra framework. At various points, we also do…

We define cohomological complexes of locally compact abelian groups associated with varieties over $p$-adic fields and prove a duality theorem under some assumption. Our duality takes the form of Pontryagin duality between locally compact…

In this paper, we develop a cohomology theory of a left-symmetric conformal algebra and study its some applications. We define the cohomology of a left-symmetric conformal algebra, and then give an isomorphism between the cohomology spaces…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

We compute bifunctors cohomology for matrix polynomials under conjugation and detect candidates for universal classes in higher invariant theory.

We prove that for generalised partitions of unity ${\phi_i \mid i \in I}$ and coverings $\mathfrak{U}:={\phi_i^{-1} (R \setminus {0}) \mid i \in I}$ of a topological space $X$ the cohomology of abstract $\mathfrak{U}$-local cochains…

We announce new methods for using prismatic cohomology to compute the K-groups of $\mathbb{Z}/p^n$ and related rings. We use computer algebra methods to compute these K-groups through a large range in specific cases and also obtain explicit…

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…

We introduce a local homology theory for linearly compact modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties such as the noetherianness, the vanishing and non-vanishing of local…

Bihom-associative algebras have been recently introduced in the study of group hom-categories. In this paper, we introduce a Hochschild type cohomology for bihom-associative algebras with suitable coefficients. The underlying cochain…

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.

Homology has long been accepted as an important computable tool for quantifying complex structures. In many applications, these structures arise as nodal domains of real-valued functions and are therefore amenable only to a numerical study…

We give a refinement of Saito's arithmetic duality for two-dimensional local rings by giving algebraic group structures for arithmetic cohomology groups.