Related papers: Kohomologie von Garben nichtabelscher Gruppen

We prove a general form of the statement that the cohomology of a quotient stack can be computed by the Borel construction. It also applies to the lisse extensions of generalized cohomology theories like motivic cohomology and algebraic…

The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the nontriviality of certain cycles of…

Let the vector bundle $\mathcal{E}$ be a deformation of the tangent bundle over the Grassmannian $G(k,n)$. We compute the ring structure of sheaf cohomology valued in exterior powers of $\mathcal{E}$, also known as the polymology. This is…

Let $A$ be an abelian sheaf on a site $X_{\tau}$ on which we have an action of a finite group $G$. Given an $A$-torsor (respectively a gerbe banded by $A$), we would like to know under what conditions it is induced from an $A^G$-torsor…

For any free oriented Borel-Moore homology theory $A$, we construct an associative product on the $A$-theory of the stack of Higgs torsion sheaves over a projective curve $C$. We show that the resulting algebra $A\mathbf{Ha}_C^0$ admits a…

We completely determine cohomology groups of sections of homogeneous line bundles over a toroidal group.

We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot-action of the Weyl group on the cohomology ring of a regular semisimple Hessenberg variety. In type A,…

Let $V$ be a finite-dimensional complex vector space. Assume that $V$ is a direct sum of subspaces each of which is equipped with a nondegenerate symmetric or skew-symmetric bilinear form. In this paper, we introduce a stratification of the…

Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the…

We construct a Leray-Serre spectral sequence for fibre bundles for de Rham sheaf cohomology on noncommutative algebras. The morphisms are bimodules with zero-curvature extendable bimodule connections. This generalises definitions involving…

We study non-abelian differentiable gerbes over stacks using the theory of Lie groupoids. More precisely, we develop the theory of connections on Lie groupoid $G$-extensions, which we call "connections on gerbes", and study the induced…

We give sharp bounds on the vanishing of the cohomology of a tensor product of vector bundles on the n-dimensional projective space in terms of the vanishing of the cohomology of the factors. For this purpose we introduce regularity indices…

In this paper we construct arithmetic analogs of the Riemann-Roch theorem and Serre's duality for line bundles. This improves on the works of Tate and van der Geer - Schoof. We define $H^0(L)$ and $H^1(L)$ as some convolution of measures…

We show that isomorphism classes $[\mathcal{A}]$ of flat $q\times q$ matrix bundles $\mathcal{A}$ (or projectively flat rank-$q$ complex vector bundles $\mathcal{E}$) on a pro-torus $\mathbb{T}$ are in bijective correspondence with the…

Condensed mathematics as developed by Clausen and Scholze yields a version of derived functors over the category of continuous $G$-modules for a Hausdorff topological group $G$. We study the resulting notion of group cohomology and its…

We explore an application of homological algebra to set theoretic objects by developing a cohomology theory for Hausdorff gaps. The cohomology theory is introduced with enough generality to be applicable to other questions in set theory.…

We study complex solvmanifolds $\Gamma\backslash G$ with holomorphically trivial canonical bundle. We show that the trivializing section of this bundle can be either invariant or non-invariant by the action of $G$. First we characterize the…

We prove that a homotopy cofinal functor between small categories induces a weak equivalence between homotopy colimits of pointed simplicial sets. This is used to prove that the non-Abelian homology of a group diagram is isomorphic to the…

Gerbes are locally connected presheaves of groupoids. They are classified up to local weak equivalence by path components in a 2-cocycle category taking values in all sheaves of groups, their isomorphisms and homotopies. If F is a full…

We look more closely at the higher nonabelian de Rham cohomology of a smooth projective variety or family of varieties that had been defined in some previous papers. We formalize using $n$-stacks the notion of shape underlying this…