Related papers: Calculations with graded perverse-coherent sheaves

We consider categories of generalized perverse sheaves, with relaxed constructibility conditions, by means of the process of gluing $t$-structures and we exhibit explicit abelian categories defined in terms of standard sheaves categories…

We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their…

We determine the non-reduced components of global nilpotent cones in various cases of interest. In particular, under the appropriate coprimality conditions, we show: (1) the global nilpotent cone for an $L$-twisted…

We consider generalizations of the Springer resolution of the nilpotent cone of a simple Lie algebra by replacing the cotangent bundle with certain other vector bundles over the flag variety. We show that the analogue of the Springer sheaf…

We study the positivity properties of the projectivization of a parabolic bundle over a smooth complex projective curve. The generators of its N\'eron--Severi group are computed, and the positive cone is determined. In particular, we…

Rost defined the Chow group of algebraic cycles with coefficients in a locally constant torsion etale sheaf. We generalize the definition to allow non-torsion coefficients. Chow groups with twisted coefficients are related to Serre's notion…

In this paper we propose a construction of generic character sheaves on reductive groups over finite local rings at even levels, whose characteristic functions are higher Deligne--Lusztig characters when the parameters are generic. We…

A quasi-coherent ringed scheme is a pair (X,A), where X is a scheme, and A is a noncommutative quasi-coherent O_X-ring. We introduce dualizing complexes over quasi-coherent ringed schemes and study their properties. For a separated…

For a reductive group over an algebraically closed field of characteristic $p > 0$ we construct the abelian category of perverse $\mathbb{F}_p$-sheaves on the affine Grassmannian that are equivariant with respect to the action of the…

We present a detailed introduction of the theory of constructible sheaf complexes in the complex algebraic and analytic setting. All concepts are illustrated by many interesting examples and relevant applications, while some important…

By Vinberg theory any homogeneous convex cone $\mathcal V$ may be realized as the cone of positive Hermitian matrices in a $T$-algebra of generalised matrices. The level hypersurfaces $\mathcal V_{q} \subset \mathcal V$ of homogeneous cubic…

Let $M(d,\chi)$ be the moduli space of semistable 1-dimensional sheaves supported at curves of degree $d$ on $\mathbb{P}^2$, with Euler characteristic $\chi$. We have the Hilbert-Chow morphism $\pi: M(d,\chi)\rightarrow |dH|$ sending each…

We study strongly graded groupoids, which are topological groupoids $\mathcal G$ equipped with a continuous, surjective functor $\kappa: \mathcal G \to \Gamma$, to a discrete group $\Gamma$, such that $\kappa^{-1}(\gamma)\kappa^{-1}(\delta)…

In this paper, we present a conjecture on the degree of unipotent characters in the cohomology of particular Deligne-Lusztig varieties for groups of Lie type, and derive consequences of it. These degrees are a necessary piece of data in the…

We give an explicit combinatorial description of the category Perv(S,N) of perverse sheaves on an oriented surface S (with boundary) with singularities at a given finite set N. The description is given in terms of any spanning graph K in S…

This paper wishes to foster communication between mathematicians and physicists working in mirror symmetry and orbifold Gromov-Witten theory. We provide a reader friendly review of the physics computation in [arXiv:hep-th/0607100] that…

Given a certain kind of linear representation of a reductive group, referred to as a quasi-symmetric representation in recent work of \v{S}penko and Van den Bergh, we construct equivalences between the derived categories of coherent sheaves…

If $X$ is a variety over a number field, Annette Huber has defined a category of "horizontal" (or "almost everywhere unramified") $\ell$-adic complexes and $\ell$-adic perverse sheaves on $X$. For such objects, the notion of weights makes…

In the present paper, we introduce two-dimensional categorified Hall algebras of smooth curves and smooth surfaces. A categorified Hall algebra is an associative monoidal structure on the stable $\infty$-category…

Let G be a reductive connected group over the algebraic closure of a finite field. In this paper we give the classification of character sheaves on G in categorical terms (as a categorical centre). Previously such a classification was known…