Related papers: Cohomology and extension problems for semi q-coron…

The purpose of this paper is to use conservative descent to study semi-orthogonal decompositions for some homogeneous varieties over general bases. We produce a semi-orthogonal decomposition for the bounded derived category of coherent…

We present a brief introduction to quantum sheaf cohomology, a generalization of quantum cohomology based on the physics of the (0,2) nonlinear sigma model.

We introduce the concept of a partial abstract kernel associated to a group G and a semilattice of groups A and relate the partial cohomology group H^3(G,C(A)) with the obstructions to the existence of admissible extensions of A by G which…

Local conditions on boundaries of $C^\infty$ Levi-flat hypersurfaces, in case the boundary is a generic submanifold, are studied. For nontrivial real analytic boundaries we get an extension and uniqueness result, which forces the…

We expand \v{C}ech cohomology of a topological space $X$ with values in a presheaf on $X$ to \v{C}ech cohomology of a commutative ring with unity $R$ with values in a presheaf on $R$. The strategy is to observe that both the set of open…

Motivated by problems in which data are given over covering generating families, we suggest a new cohomology theory for diffeological spaces, called diffeological \v{C}ech cohomology, which is an exact $ \partial $-functor of the section…

We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…

We prove that the cohomology groups of an etale Q_p-local system on a smooth proper rigid analytic space are finite-dimensional Q_p-vector spaces, provided that the base field is either a finite extension of Q_p or an algebraically closed…

Given a quasi-compact, quasi-separated scheme X, a bijection between the tensor localizing subcategories of finite type in Qcoh(X) and the set of all subsets $Y\subseteq X$ of the form $Y=\bigcup_{i\in\Omega}Y_i$, with $X\setminus Y_i$…

We consider the derived category of coherent sheaves on a complex vector space equivariant with respect to an action of a finite reflection group G. In some cases, including Weyl groups of type A, B, G_2, F_4, as well as the groups…

In this note we extend the main results of [E. Enochs and S. Estrada, Relative homological algebra in the category of quasi-coherent sheaves. Adv. in Math. 194(2005), 284-295] to the category of cartesian modules over a flat presheaf of…

We consider a class of non-convex cones $V$ in $\mathbb{R}^n$ which can be presented as (not unique) union of convex cones of some codimension $q$ which we call the index of non-convexity. This class contains non-convex symmetric…

Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $q$-partial differential equations, then, it can be expanded in terms of the product of…

Let X be e quasi-compact and semi-separated scheme. If every at quasi- coherent sheaf has finite cotorsion dimension, we prove that X is n-perfect for some n > 0. If X is coherent and n-perfect(not necessarily of finite krull dimension), we…

In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it…

We describe an explicit semi-algebraic partition for the complement of a real hyperplane arrangement such that each piece is contractible and so that the pieces form a basis of Borel-Moore homology. We also give an explicit correspondence…

This paper is the first in a series. The main goal of the series is to present a geometric construction of certain remarkable tensor categories arising from quantum groups coresponding to the value of deformation parameter $q$ equal to a…

On any pure $n$-dimensional, possibly non-reduced, analytic space $X$ we introduce the sheaves $\mathscr{E}_X^{p,q}$ of smooth $(p,q)$-forms and certain extensions $\mathscr{A}_X^{p,q}$ of them such that the corresponding Dolbeault complex…

Contents * Introduction -- Why $S^1$-extended phase space? -- Why central extensions of classical symmetries? * Central extension \Gt of a group $G$ -- Group cohomology -- Cohomology and contractions: Pseudo-cohomology -- Principal bundle…

In this article, we obtain quasiconformal extensions of some classes of conformal maps defined either on the unit disc or on the exterior of it onto the extended complex plane. Some of these extensions have been obtained by constructing…