Related papers: Brief Notes on Sheaves Theory

We give a formalism of mixed sheaves on varieties over a subfield of the complex number field.

Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…

A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…

This is an introduction to the notion of local subgroupoid introduced by the author and R. Brown. It can also serve as an introduction to an application of sheaf theory, and so could be useful to beginners in that theory. The main results…

We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…

This is an overview (in french) of the Theory of Species for a general audience. Basic notions are introduced in a non too technical manner, with an explanation of why should one approach the notion of discrete structures in this particular…

"Theory figures" are a staple of theoretical visualization research. Common shapes such as Cartesian planes and flowcharts can be used not only to explain conceptual contributions, but to think through and refine the contribution itself.…

We extend the theory of fields/distributions developed the paper "A Feigin-Frenkel theorem with n singularities" to a general base scheme. In order to do so we introduce suitable notions of topological sheaves on schemes and study their…

We study fundamental forms of algebraic varieties using the sheaves of principal parts of line bundles and establish a vanishing theorem for any order fundamental forms. We also give connection of fundamental forms with the higher order…

This is a review article based on a mini-course comprised of four talks given by the author at Berkeley.

We introduce and study configuration schemes, which are obtained by ``glueing'' usual schemes along closed embeddings. The category of coherent sheaves on a configuration scheme is investigated. Smooth configuration schemes provide…

This article is the second part in the series of articles where we are developing theory of valuations on manifolds. Roughly speaking valuations could be thought as finitely additive measures on a class of nice subsets of a manifold which…

In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their derived generalizations.

Moduli spaces of stable sheaves on smooth projective surfaces are in general singular. Nonetheless, they carry a virtual class, which -- in analogy with the classical case of Hilbert schemes of points -- can be used to define intersection…

The article is devoted to linear quasigroups and some of their generalizations. In the first part main definitions and notions of the theory of quasigroups are given. In the second part some elementary properties of linear quasigroups and…

The purpose of this paper is to propose a sheaf theoretic approach to the theory of quantum principal bundles over non affine bases. We study the quantization of principal bundles G -> G/P, where G is a semisimple group and P a parabolic…

This short survey presents the essential features of what is called Painlev\'e analysis, i.e. the set of methods based on the singularities of differential equations in order to perform their explicit integration. Full details can be found…

We expand the toolbox of (co)homological methods in computational topology by applying the concept of persistence to sheaf cohomology. Since sheaves (of modules) combine topological information with algebraic information, they allow for…

In this note we examine a natural concept of a curve on a supermanifold and the subsequent notion of the jet of a curve. We then tackle the question of geometrically defining the higher order tangent bundles of a supermanifold. Finally we…

We discuss relations between the motives of two varieties with equivalent derived categories of coherent sheaves.