Related papers: Staggered sheaves on partial flag varieties

Let $A$ be a graded algebra. It is shown that the derived category of dg modules over $A$ (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orbit category of the derived category of graded $A$-modules.…

Originally a technical tool, the derived category of coherent sheaves over an algebraic variety has become over the last twenty years an important invariant in the birational study of algebraic varieties. Problems of birational invariance…

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.

Let X be a smooth toric variety defined by the fan {\Sigma} . We consider {\Sigma} as a finite set with topology and define a natural sheaf of graded algebras A_{\Sigma} on {\Sigma} . The category of modules over A_{\Sigma} is studied…

Given an action of a finite group on a triangulated category, we investigate under which conditions one can construct a linearised triangulated category using DG-enhancements. In particular, if the group is a finite group of automorphisms…

We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…

We define a variety of doubly indexed flags, this is a smooth, projective variety, and we describe it as an iterated over Grassmannian varieties. On the other hand, we consider the variety of partial flags which are stabilized by a given…

We prove sign-alternation of the product structure constants in the basis dual to the basis consisting of the structure sheaves of Schubert varieties in the torus-equivariant Grothendieck group of coherent sheaves on the partial flag…

This paper is based on a talk at a conference "JDG 2017: Conference on Geometry and Topology". We survey recent progress on the DK hypothesis connecting the birational geometry and the derived categories stating that the K-equivalence of…

We calculate a semi-orthogonal decomposition of the bounded derived category of coherent sheaves on P(1,1,1,3) using a tilting bundle.

Given a smooth variety $X$ with an action of a finite group $G$, and a semiorthogonal decomposition of the derived category, $\mathcal{D}([X/G])$, of $G$-equivariant coherent sheaves on $X$ into subcategories equivalent to derived…

G-structures and Cartan geometries are two major approaches to the description of geometric structures (in the sense of differential geometry) on manifolds of some fixed dimension $n$. We show that both descriptions naturally extend to the…

Naisse and Vaz defined an extension of KLR algebras to categorify Verma modules. We realise these algebras geometrically as convolution algebras in Borel-Moore homology. For this we introduce Grassmannian-Steinberg quiver flag varieties.…

We introduce the notion of a quasicoherent sheaf on a complex noncommutative two-torus $T$ as an ind-object in the category of holomorphic vector bundles on $T$. Extending the results of math.QA/0211262 and math.QA/0308136 we prove that the…

We study derived categories of coherent sheaves on abelian varieties. We give a criterion for the equivalence of the derived categories on two abelian varieties. We describe the autoequivalence group for the derived category of coherent…

Graded vector bundles over a given $\mathbb{Z}$-graded manifold can be defined in three different ways: certain sheaves of graded modules over the structure sheaf of the base graded manifold, finitely generated projective graded modules…

We give a complete description of the group of exact autoequivalences of the bounded derived category of coherent sheaves on a K3 surface of Picard rank 1. We do this by proving that a distinguished connected component of the space of…

A semiorthogonal decomposition for the bounded derived category (the category of perfect complexes in a non smooth case) of coherent sheaves on a Brauer Severi scheme is given. It relies on bounded derived categories (categories of perfect…

For a stratified topological space we introduce the category of IC-modules, which are linear algebra devices with the relations described by the equation d^2=0. We prove that the category of (mixed) IC-modules is equivalent to the category…

We characterize $t$-structures in stable $\infty$-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathfrak{t}$ on a stable $\infty$-category $\mathbf{C}$ is equivalent to a normal…