Related papers: Perverse schobers and wall crossing

For each positive rational number $\epsilon$, we define $K$-theoretic $\epsilon$-stable quasimaps to certain GIT quotients $W\sslash G$. For $\epsilon>1$, this recovers the $K$-theoretic Gromov-Witten theory of $W\sslash G$ introduced in…

We produce full strong exceptional collections consisting of vector bundles on the geometric invariant theory quotient of certain linear actions of a split reductive group $G$ of rank two. The vector bundles correspond to irreducible…

In this paper we study the Witt groups of symmetric and anti-symmetric forms on perverse sheaves on a finite-dimensional topologically stratified space with even dimensional strata. We show that the Witt group has a canonical decomposition…

In this paper, we prove a window theorem for categorical Donaldson-Thomas theories on local surfaces as an analogue of window theorem for GIT quotient stacks. We give two applications of our main result. The first one is a proof of…

In math.RT/0201073 we constructed an equivalence between the derived category of equivariant coherent sheaves on the cotangent bundle to the flag variety of a simple algebraic group and a (quotient of) the category of constructible sheaves…

This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme $X$ of prime characteristic. The main result is that when the Frobenius map on $X$ is finite, for any compact generator $G$ of…

In the strict semi stable reduction situation, we describe the various filtrations of the perverse sheaf of nearby cycles in terms of irreducible perverse sheaves together with the action of the monodromy operator. We then study the…

For a weighted projective line X, a wide subcategory of the category coh-X of coherent sheaves over X is called c-invariant if it is closed under the grading shift of the canonical element c. We proved that a c-invariant wide subcategory of…

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…

In [arXiv:2008.04625] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact K\"ahler manifold using analytic GIT theory. The aim of this article is to show that this classifying space taken in…

We define a new perverse t-exact pullback operation on derived categories of constructible sheaves which generalizes most perverse t-exact functors in sheaf theory, such as microlocalization, the Fourier-Sato transform and vanishing cycles.…

Given a double quiver, we study homological algebra of twisted quiver sheaves with the moment map relation using the short exact sequence of Crawley-Boevey, Holland, Gothen, and King. Then in a certain one-parameter space of the stability…

In this paper we prove that the category of parity complexes on the flag variety of a complex connected reductive group is a "graded version" of the category of tilting perverse sheaves on the flag variety of the dual group, for any field…

We prove the existence of semiorthogonal decompositions of derived categories of Quot schemes of zero-dimensional quotients on curves in terms of derived categories of symmetric products of curves. The above result is a categorical analogue…

We give a generalization, in the context of sheaves, of a classical result of Grothendieck concerning the integrability of connections of type $(0,1)$ over a ${\cal C}^{\infty}$ vector bundle over a complex manifold. We introduce the notion…

Graded Hecke algebras can be constructed geometrically, with constructible sheaves and equivariant cohomology. The input consists of a complex reductive group G (possibly disconnected) and a cuspidal local system on a nilpotent orbit for a…

We study the spectrum of closed subcategories in a quasi-scheme, i.e. a Grothendieck category $X$. The closed subcategories are the direct analogs of closed subschemes in the commutative case, in the sense that when $X$ is the category of…

Wall-crossing formulas for various flavors of elliptic genus can be obtained using master spaces. We give a topological criterion which implies that such wall-crossing formulas are trivial. Applications are given for: GIT quotients,…

In characteristic zero, Bezrukavnikov has shown that the category of perverse coherent sheaves on the nilpotent cone of a simply connected semisimple algebraic group is quasi-hereditary, and that it is derived-equivalent to the category of…

A criterion for a functor between derived categories of coherent sheaves to be full and faithful is given. A semiorthogonal decomposition for the derived category of coherent sheaves on the intersection of two even dimensional quadrics is…