Related papers: Perverse coherent sheaves (after Deligne)

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…

This is a mostly expository paper, intended to explain a very natural relationship between two a priori distinct notions appearing in the literature: Generic Vanishing in the context of vanishing theorems and birational geometry, and…

We give a description of certain categories of equivariant coherent sheaves on Grothendieck's resolution in terms of the categorical affine Hecke algebra of Soergel. As an application, we deduce a relationship of these coherent sheaf…

Fix a scheme $X$ over a field of characteristic zero that is equipped with an action of a reductive algebraic group $G$. We give necessary and sufficient conditions for a $G$-equivariant coherent sheaf on $X$ or a bounded-above complex of…

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 simple simply connected complex algebraic group and let $\mathfrak{g}_*$ be a $\mathbf{Z}/m$-grading on its Lie algebra $\mathfrak{g}$. In a recent series of articles, G. Lusztig and Z. Yun, studied the classification of simple…

For a balanced wall crossing in geometric invariant theory, there exist derived equivalences between the corresponding GIT quotients if certain numerical conditions are satisfied. Given such a wall crossing, I construct a perverse sheaf of…

Let $X$ be a topologically stratified space, $p$ be any perversity on $X$, and $k$ be a field. We show that the category of $p$-perverse sheaves on $X$, constructible with respect to the stratification and with coefficients in $k$, is…

We construct a co-$t$-structure on the derived category of coherent sheaves on the nilpotent cone $\mathcal{N}$ of a reductive group, as well as on the derived category of coherent sheaves on any parabolic Springer resolution. These…

Achar has recently introduced a family of t-structures on the derived category of equivariant coherent sheaves on a $G$-scheme, generalizing the perverse coherent t-structures of Bezrukavnikov and Deligne. They are called \emph{staggered}…

A quasi-coherent ringed scheme is a pair (X,A), where X is a scheme, and A is a noncommutative quasi-coherent O_X-ring. We introduce dualizing complexes over quasi-coherent ringed schemes and study their properties. For a separated…

Constructible sheaves of abelian groups on a stratified space can be equivalently described in terms of representations of the exit-path category. In this work, we provide a similar presentation of the abelian category of perverse sheaves…

The notions of consistent pairs and consistent chains of t-structures are introduced. A theorem that two consistent chains of t-structures generate a distributive lattice is proven. The technique developed is then applied to the pairs of…

Intersection cohomology is a way to enhance classical cohomology, allowing us to use a famous result called Poincar\'e duality on a large class of spaces known as stratified pseudomanifolds. There is a theoretically powerful way to arrive…

In this paper, which is mostly a research announcement, we give a new algebraic construction of knot contact homology in the sense of L. Ng [Ng05a]. For a link $L$ in $ {\mathbb R}^3 $, we define a differential graded (DG) $k$-category $…

We generalize the construction given in math.AG/0309435 of a "constant" t-structure on the bounded derived category of coherent sheaves $D(X\times S)$ starting with a t-structure on $D(X)$. Namely, we remove smoothness and quasiprojectivity…

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…

We introduce irregular constructible sheaves, which are $\mathbb{C}$-constructible with coefficients in a finite version of Novikov ring $\Lambda$ and special gradings. We show that the bounded derived category of cohomologically irregular…

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…

We introduce a class of perverse sheaves on a partial flag manifold of a connected reductive group G defined over a finite field which are equivariant under the action of the group of rational points of G. The definition of this class is…