Related papers: Cech cohomology over $\mathbb{F}_{1^2}$

We develop a new cohomology theory for finite-dimensional left-symmetric color algebras and their finite-dimensional bimodules, establishing a connection between Lie color cohomology and left-symmetric color cohomology. We prove that the…

Let $A$ be a Banach algebra and $M$ be a Banach right $A$-module. A linear map $\delta : M\to M$ is called a generalized derivation if there exists a derivation $d : A \to A$ such that $$\delta(xa)=\delta(x)a + x d(a) \quad (a \in A, x \in…

In a previous paper, the authors showed that the category of E(n)_*E(n)-comodules is a localization of the category of BP_*BP-comodules. In this paper, we study the resulting localization functor L_n on the category of BP_*BP-comodules. It…

We generalize and clarify Gerstenhaber and Schack's "Special Cohomology Comparison Theorem". More specifically we obtain a fully faithful functor between the derived categories of bimodules over a prestack over a small category U and the…

Sheaf cohomology or, more generally, higher direct images of coherent sheaves along proper morphisms are central to modern algebraic geometry. However, the computation of these objects is a non-trivial and expensive task which easily…

The aim of this paper is to study the cohomology theory of monoid schemes in general and apply it to vector and line bundles. We will prove that over separated monoid schemes, any vector bundle is a coproduct of line bundles and then go on…

This is my diploma thesis in german language. In the context of formal deformation theorie of assoziative observables in classical field theory I consider the symmetric algebra S(V) on an arbitrary-dimensional R- or C-vectorspace V as a…

A quandle equipped with a good involution is referred to as symmetric. It is known that the cohomology of symmetric quandles gives rise to strong cocycle invariants for classical and surface links, even when they are not necessarily…

Looking at the cartesian product of a topological space with itself, a natural map to be considered on that object is the involution that interchanges the coordinates, i.e. that maps (x,y) to (y,x). The so-called halfsquaring construction,…

In this work we construct an extension for the category of 0-modules by analogy with [H.-J. Baues and G. Wirshing, Cohomology of small categories, J. Pure Appl. Algebra, 38(1985), 187-211]. The 0-cohomology functor becomes a derived functor…

Arithmetic duality theorems over a local field $k$ are delicate to prove if $\mathrm{char} k > 0$. In this case, the proofs often exploit topologies carried by the cohomology groups $H^n(k, G)$ for commutative finite type $k$-group schemes…

Given a vector bundle $F$ on a variety $X$ and $W\subset H^0(F)$ such that the evaluation map $W\otimes \mathcal{O}_X\to F$ is surjective, its kernel $S_{F,W}$ is called generalized syzygy bundle. Under mild assumptions, we construct a…

We show that the cohomology table of any coherent sheaf on projective space is a convergent--but possibly infinite--sum of positive real multiples of the cohomology tables of what we call supernatural sheaves.

An Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra A_h generated by elements x,y, which satisfy yx-xy = h, where h is in F[x]. When h is…

By a result of Gerstenhaber and Schack the simplicial cohomology ring $H^*(\mathcal{C};k)$ of a poset $\mathcal{C}$ is isomorphic to the Hochschild cohomology ring $HH^*(k\mathcal{C})$ of the category algebra $k\mathcal{C}$, where the poset…

We extend our work in~\cite{rm01} to the case of Hopf comodule coalgebras. We introduce the cocylindrical module $C \natural^{} \mathcal{H}$, where $\mathcal{H}$ is a Hopf algebra with bijective antipode and $C$ is a Hopf comodule coalgebra…

Let $G$ be a connected split reductive group over a finite field ${\mathbb F}_q$ and $X$ a smooth projective geometrically connected curve over ${\mathbb F}_q$. The $\ell$-adic cohomology of stacks of $G$-shtukas is a generalization of the…

We show that for any constructible sheaf F on a smooth algebraic variety X over a field of arbitrary characteristic its singular support SS(F) is equidimensional of dimension dim X. Here SS(F) is the minimal closed subset of the cotangent…

Let $n \geq 1$ be an integer, let $V=(\mathbb{Z}/2\mathbb{Z})^{n}$ and let $X$ be a $V$-CW-complex. If $X$ is a finite $CW$-complexe, the equivariant modulo $2$ cohomology of the $V$-CW-complexe $X$, denoted by $H_{V}^{*}(X,…

We show that the hypercohomology of the Chevalley-Eilenberg-de Rham complex of a Lie algebroid L over a scheme with coefficients in an L-module can be expressed as a derived functor. We use this fact to study a Hochschild-Serre type…