Related papers: Mixed modular perverse sheaves on affine flag vari…

We construct period sheaves for Hamiltonian spaces, as conjectured in the work of Ben-Zvi, Sakellaridis and Venkatesh, using the perverse pullback functors introduced in the authors' previous work. We prove a dimensional reduction…

In this paper we develop the theory of perverse sheaves on Artin stacks continuing the study in "The six operations for sheaves on Artin stacks I: Finite Coefficients" and "The six operations for sheaves on Artin stacks II: Adic…

We exhibit gluing properties of cluster tilting subcategories in exact $\infty$-categories within the framework of perverse schobers on surfaces with boundary. These results are based on a study of the restriction functors from global…

We define an affine Jacquet functor and use it to describe the structure of induced affine Harish-Chandra modules at noncritical levels, extending the theorem of Kac and Kazhdan [KK] on the structure of Verma modules in the…

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 introduce, on a topological space X, a class of stacks of abelian categories we call "stacks of type P." This class of stacks includes the stack of perverse sheaves (of any perversity, constructible with respect to a fixed…

Continuing the study of perverse sheaves on the nilpotent cone of a $\mathbb{Z}/m$-graded Lie algebra initiated by Lusztig--Yun, we study in this work the parabolic induction and introduce the notion of supercuspidal sheaves on the…

Using techniques of [BKV], we construct a perverse t-structure on the infinity-category of l-adic LG-equivariant sheaves on the regular-semisimple bounded locus of the loop group LG and prove that the derived $\tau$-coinvariants of affine…

Let G be a split semisimple linear algebraic group over a field k0. Let E be a G-torsor over a field extension k of k0. Let h be an algebraic oriented cohomology theory in the sense of Levine-Morel. Consider a twisted form E/B of the…

We show that the Borel-equivariant derived category of sheaves on the flag variety of a complex reductive group is equivalent to the perfect derived category of dg modules over the extension algebra of the direct sum of the simple…

We show that perverse character varieties are (quasi-)affine. We do this in a purely stack-theoretic fashion, by exhibiting enough sections of the structure sheaf.

Perverse schobers are categorical analogs of perverse sheaves. Examples arise from varieties admitting flops, determined by diagrams of derived categories of coherent sheaves associated to the flop: in this paper we construct mirror…

We prove that the category of equivariant perverse sheaves on the affine Grassmannian of PGL(2, R) is highest weight and we construct the projective objects. Moreover we prove that the category of perverse sheaves on the odd component is…

We prove that for extended Dynkin quivers, simple perverse sheaves in Lusztig category are characterized by the nilpotency of their singular support. This proves a conjecture of Lusztig in the case of affine quivers. For cyclic quivers, we…

Cohesive modules give a dg-enhancement of the bounded derived category of coherent sheaves on a complex manifold via superconnections. In this paper we discuss the deformation theory of cohesive modules on compact complex manifolds. This…

Hoffstein and Hulse recently introduced the notion of shifted convolution Dirichlet series for pairs of modular forms $f_1$ and $f_2$. The second two authors investigated certain special values of symmetrized sums of such functions, numbers…

The famous Kazhdan-Lusztig Conjecture of the 1970s states that the multiplicity of an irreducible composition factor of a Verma module can be computed by evaluating Kazhdan-Lusztig polynomials at 1. Thus the character of a Verma module is a…

We prove Soergel's conjecture on the characters of indecomposable Soergel bimodules. We deduce that Kazhdan-Lusztig polynomials have positive coefficients for arbitrary Coxeter systems. Using results of Soergel one may deduce an algebraic…

We develop a unified approach for identifying spaces of stability conditions of triangulated categories arising from weighted marked surfaces with moduli spaces of quadratic differentials. This approach is based on the notion of a perverse…

The convolution powers of a perverse sheaf on an abelian variety define an interesting family of branched local systems whose geometry is still poorly understood. We show that the generating series for their generic rank is a rational…