Related papers: Chiral Janus complexes
In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective variety.
Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.
The space of global sections of the chiral de Rham complex on any closed complex curve with genus $g \ge2$ is calculated.
We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The discussion of the variational (bi)complex is set up in…
This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.
The existence of an infinite set of conserved currents in completely integrable classical models, including chiral and Toda models as well as the KP and self-dual Yang-Mills equations, is traced back to a simple construction of an infinite…
We characterize injective objects, injective hulls and essential embeddings in the category of symmetric categories enriched in a small, integral and involutive quantaloid. In particular, injective partial metric spaces are precisely…
Several authors have introduced various type of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In [2], several coherent-like…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
This is a complete classification of the complex forms of quaternionic symmetric spaces
Using group theoretical methods, we enumerate possible chiral representations in which hadron interpolating currents can be classified. We give simple examples of currents in each representation, some of which are well known. The…
Using the theory infinity-categories we construct derived (dg-)categories of regular, holonomic D-modules and algebraically constructible sheaves on a complex smooth algebraic stack. We construct a natural infinity-categorical equivalence…
We extend some of the results of Bondal-Orlov on the equivalence of derived categories to the case of orbifolds by using the category of coherent orbifold sheaves.
A new section on projections of coherent sheaves from a projective space to a lower-dimensional projective space has been added. Also some of the notation has been altered to bring it into line with the joint paper with Eisenbud and…
Abstract polytopes are combinatorial objects that generalise geometric objects such as convex polytopes, maps on surfaces and tilings of the space. Chiral polytopes are those abstract polytopes that admit full combinatorial rotational…
In this paper we prove that the dimension of the bounded derived category of coherent sheaves on a smooth quasi-projective curve is equal to one. We also discuss dimension spectrums of these categories.
We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…
In this survey, we discuss whether the complex projective space can be characterized by its integral cohomology ring among compact complex manifolds.
We extend Orlov's result on representability of equivalences to schemes projective over a field. We also investigate the quasi-projective case.
We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…