Related papers: Groupoid sheaves as quantale sheaves

We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…

We construct a new class of finite-dimensional C^*-quantum groupoids at roots of unity q=e^{i\pi/\ell}, with limit the discrete dual of the classical SU(N) for large orders. The representation category of our groupoid turns out to be tensor…

Let G be a simple simply-connected group over an algebraically closed field k, X be a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on the moduli stack Bun_G of G-torsors on X…

We define a categorical action of the shifted quantum loop group of $\mathfrak{sl}_2$ on the derived categories of Quot schemes of finite length quotient sheaves on a smooth projective curve. As an application, we obtain a semi-orthogonal…

Let A be a finitely generated connected graded k-algebra defined by a finite number of monomial relations. Then there is a finite directed graph, Q, the Ufnarovskii graph of A, for which the categories QGr(A) and QGr(kQ) are equivalent:…

In a previous paper, we constructed a category of (phi, Gamma)-modules associated to any adic space over Q_p with the property that the etale (phi, Gamma)-modules correspond to etale Q_p-local systems; these involve sheaves of period rings…

Let kQ be the path algebra of a quiver Q with its standard grading. We show that the category of graded kQ-modules modulo those that are the sum of their finite dimensional submodules, QGr(kQ), is equivalent to several other categories: the…

We study the equivariant sheaf counting theory on K3 surfaces with finite group actions. Let $\sS=[S/G]$ be a global quotient stack, where $S$ is a K3 surface and $G$ is a finite group acting as symplectic homomorphisms on $S$. We show that…

In this expository note, we discuss some results of the author on the structure of derived categories of equivariant coherent sheaves and the derived categories of geometric invariant theory quotients. We take a recent perspective,…

We give an existence result on (H,A)-stable sheaves on a K3 or abelian surface X with primitive triple of invariants (rank,first Chern class,Euler characteristics) in the integral cohomology lattice. Such a result yields the existence of…

We prove an equivariant Grothendieck-Ogg-Shafarevich formula. This formula may be viewed as an \'etale analogue of well-known formulas for Zariski sheaves generalizing the classical Chevalley-Weil formula. We give a new approach to those…

We study a category of semiinfinite sheaves on the affine flag variety of a connected reductive algebraic group, with coefficients in a field of arbitrary characteristic, generalizing some results of Gaitsgory and showing that this category…

We construct an equivalence of graded Abelian categories from a category of representations of the quiver-Hecke algebra of type $A_1^{(1)}$ to the category of equivariant perverse coherent sheaves on the nilpotent cone of type $A$. We prove…

Continuing our previous work on graded twisting of Hopf algebras and monoidal categories, we introduce a graded twisting construction for equivariant comodule algebras and module categories. As an example we study actions of quantum…

Stably supported quantales generalize pseudogroups and provide an algebraic context in which to study the correspondences between inverse semigroups and \'etale groupoids. Here we study a further generalization where a non-unital version of…

Let L be a finite field extension of Q_p and let G be the group of L-rational points of a split connected reductive group over L. We view G as a locally L-analytic group with Lie algebra g. We define a functor from admissible locally…

We present an explicit expression of the cohomology complex of a constructible sheaf of abelian groups on the small \'etale site of an irreducible curve over an algebraically closed field, when the torsion of the sheaf is invertible in the…

When a reductive group $G$ acts linearly on a complex projective scheme $X$ there is a stratification of $X$ into $G$-invariant locally closed subschemes, with an open stratum $X^{ss}$ formed by the semistable points in the sense of…

Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of…

Let $G$ be a semisimple algebraic group over an algebraically closed field $k$, whose characteristic is positive and does not divide the order of the Weyl group of $G$, and let $\breve G$ be its Langlands dual group over $k$. Let $C$ be a…