Related papers: Perverse Schobers

Kapranov and schechtman gave quiver description of perverse sheaves on real hyperplane arrangements. We used this description to relate the perverse sheaves on Coxeter hyperplane arrangements of type $\mathcal A_n$ for different values of…

We prove a conjecture of Lusztig on a microlocal characterization of his perverse sheaves. For any finite quiver without loops, an equivariant simple perverse sheaf on the variety of quiver representations is a Lusztig's perverse sheaf if…

On a complex contact manifold, or complex symplectic manifold with weight-1 circle action, we construct a sheaf of stable categories carrying a t-structure which is locally equivalent to a microlocalization of the perverse t-structure.

We study a one parameter degeneration of Calabi Yau threefolds whose central fiber contains a single ordinary double point. Using the nearby and vanishing cycle formalism, we construct a canonical perverse object on the singular fiber from…

In this article we consider the general definition of Lustig sheaves for arbitrary quivers, possibly carrying loops. We answer a conjecture raised by Lusztig asking if the more "simple" Lusztig perverse sheaves are enough to span the whole…

We propose the notion of perverse coherent sheaves for symplectic singularities and study its properties. In particular, it gives a basis of simple objects in the Grothendieck group of Poisson sheaves. We show that perverse coherent bases…

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…

We consider the space Z(C,L) of 0-cycles on the complex line C with coefficients in a commutative monoid L subject to certain conditions. Such spaces include the symmetric products (for L=Z_+) and the Ran space (for L=T={ True, False} being…

We consider a hyperplane arrangement in $\mathbb{C}^n$ defined over $\mathbb{R}$, and the associated natural stratification of $\mathbb{C}^n$. The category of perverse sheaves smooth with respect to this stratification was described by…

The study of Haeflier suggests that it is natural to regard a pseudogroup as an etale groupoid. We show that any etale groupoid corresponds to a pseudogroup sheaf, a new generalization of a pseudogroup. This correspondence is an analog of…

In the first section we study a functor of Bezrukavnikov, Finkelberg and Ostrik defined on character sheaves; we compute it in a Grothendieck group taking weights into account. In the second section we enlarge the class of character sheaves…

Under some assumptions we prove that the Deligne tensor product of categories of constructible perverse sheaves on pseudomanifolds X and Y is the category of constructible perverse sheaves on X\times Y. The Deligne external tensor product…

We give an explicit construction of the stack of microlocal perverse sheaves on the projective cotangent bundle of a complex manifold. Microlocal perverse sheaves will be represented as complexes of analytic ind-sheaves which have recently…

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…

This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse $t$-structure on the derived category of coherent sheaves on a Noetherian scheme with a dualizing complex. Construction extends…

Let H be an arrangement of hyperplanes in R^n and Perv(C^n,H) be the category of perverse sheaves on C^n smooth with respect to the stratification given by complexified flats of H. We give a description of Perv(C^n,H) in terms of "matrix…

We introduce and study the category of modular (i.e. with coefficient of positive characteristic) monodromic perverse sheaves on complex stratified $T$-varieties, with $T$ a complex algebraic torus. In particular, we show that under…

Perverse-Hodge complexes are objects in the derived category of coherent sheaves obtained from Hodge modules associated with Saito's decomposition theorem. We study perverse-Hodge complexes for Lagrangian fibrations and propose a symmetry…

We define a stratification of the moduli stack of coherent sheaves on an elliptic curve which allows us (1) to give an explicit description of the irreducible components of the global nilpotent cone of elliptic curves, (2) to establish an…

This survey paper, based on a talk at the International Congress of Basic Science in Beijing in July 2025, summarizes joint work of the authors with M. Kontsevich [1408.2673] establishing the relation between the ``Algebra of the Infrared"…