Related papers: Perverse pullbacks

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…

We consider the category of perverse sheaves on a complex vector space smooth with respect to a stratification given by an arrangement of hyperplanes with real equations. As shown in an earlier wotk of two of the authors, this category can…

In their article "Elementary construction of perverse sheaves", R.MacPherson and K. Vilonen show that on a Thom-Mather space X the category PervX of perverse sheaves is equivalent to the category C(F, G, T) whose objects are data of…

We define and study a relative perverse $t$-structure associated with any finitely presented morphism of schemes $f: X\to S$, with relative perversity equivalent to perversity of the restrictions to all geometric fibres of $f$. The…

We show that the inverse Serre functor for the constructible derived category $\mathbf{D}^\mathrm{b}_\mathrm{c}(\mathbb{P}^n)$ is given by the $\mathbb{P}$-twist at the simple perverse sheaf corresponding to the open stratum. Moreover, we…

Perverse schobers are categorifications of perverse sheaves. We construct a perverse schober on a partial compactification of the stringy K\"ahler moduli space (SKMS) associated by Halpern-Leistner and Sam to a quasi-symmetric…

We suggest a possibility for a categorical generalization of the concept of a perverse sheaf, in which vector spaces are replaced by triangulated categories. We call such hypothetical objects perverse Schobers and consider several examples,…

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…

In this paper, we construct proper pushforwards and flat pullbacks in Chow groups of coherent sheaf stacks over a Deligne-Mumford(DM) stack. When there is a relative semi-perfect obstruction theory for a DM-type morphism $X \to Y$, $X$ is a…

We study perverse sheaves of categories their connections to classical algebraic geometry. We show how perverse sheaves of categories encode naturally derived categories of coherent sheaves on $\mathbb{P}^1$ bundles, semiorthogonal…

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.

It is usually not straightforward to work with the category of perverse sheaves on a variety using only its definition as a heart of a $t$-structure. In this paper, the category of perverse sheaves on a smooth toric variety with its orbit…

Let $pi:X\to\Delta$ be a one-parameter degeneration whose central fiber $X_0$ has a single ordinary double point. The nearby- and vanishing-cycle formalism determines a canonical perverse sheaf on $X_0$, obtained from the variation morphism…

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…

Let X be a scheme of finite type over a Noetherian base scheme S admitting a dualizing complex, and let U be an open subset whose complement has codimension at least 2. We extend the Deligne-Bezrukavnikov theory of perverse coherent sheaves…

The goal of this work is to construct a perverse t-structure on the infinity-category of l-adic LG-equivariant sheaves on the loop Lie algebra Lg and to show that the affine Grothendieck-Springer sheaf S is perverse. Moreover, S is an…

We develop the theory of semi-orthogonal decompositions and spherical functors in the framework of stable $\infty$-categories. Building on this, we study the relative Waldhausen S-construction $S_\bullet(F)$ of a spherical functor $F$ and…

Inspired by symplectic geometry and a microlocal characterizations of perverse (constructible) sheaves we consider an alternative definition of perverse coherent sheaves. We show that a coherent sheaf is perverse if and only if…

This paper is an introduction to the use of perverse sheaves with positive characteristic coefficients in modular representation theory. In the first part, we survey results relating singularities in finite and affine Schubert varieties and…

The titular, foundational work of Beilinson not only gives a technique for gluing perverse sheaves but also implicitly contains constructions of the nearby and vanishing cycles functors of perverse sheaves. These constructions are…