Related papers: Artin perverse 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…

Let $Z\to X$ be a closed immersion of smooth affine schemes over an arbitrary field $k$, and $X^h_Z$ denote the henselization of $X$ along $Z$. For each presheaf $E\colon \mathbf{SH}(k)\to \mathrm{Ab}^\mathrm{op}$ on the stable motivic…

Starting from a real analytic conformal Cartan connection on a real analytic surface $S$, we construct a complex surface $T$ containing a family of pairs of projective lines. Using the structure on $S$ we also construct a complex $3$-space…

Let $\mathcal{G}$ be a Grothendieck category, let $\mathbf{t}=(\mathcal{T},\mathcal{F})$ be a torsion pair in $\mathcal{G}$ and let $(\mathcal{U}_\mathbf{t},\mathcal{W}_\mathbf{t})$ be the associated Happel-Reiten-Smal$\o$ t-structure in…

The present paper focuses on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the finest t-stability on a piecewise hereditary triangulated…

The geometric Satake isomorphism is an equivalence between the categories of spherical perverse sheaves on affine Grassmanian and the category of representations of the Langlands dual group. We provide a similar description for derived…

We give a purely geometric categorification of tensor products of finite-dimensional simple $U_q(sl_2)$-modules and $R$-matrices on them. The work is developed in the framework of category of perverse sheaves and the categorification…

We generalize fundamental notions of higher algebra, traditionally developed within the $\infty$-category of spectra, to the broader setting of $t$-structured tensor triangulated $\infty$-categories ($ttt$-$\infty$-categories). Under a…

On an $n$-dimensional locally reduced complex analytic space $X$ on which the shifted constant sheaf $\Q_X^\bullet[n]$ is perverse, it is well-known that, locally, $\Q_X^\bullet[n]$ underlies a mixed Hodge module of weight $\leq n$ on $X$,…

An intrinsic construction of the tensor category of finite dimensional representations of the Langlands dual group of G in terms of a tensor category of perverse sheaves on the loop group, LG, is given. The construction is applied to the…

We develop a theory of completeness for weight structures on stable categories, dual to the theory of complete t-structures. As in the bounded case, we show that complete weight structures are determined by their weight heart, giving rise…

We provide a uniform construction of "mixed versions" or "graded lifts" in the sense of Beilinson-Ginzburg-Soergel which works for arbitrary Artin stacks. In particular, we obtain a general construction of graded lifts of many categories…

Motivated by the polynomial representation theory of the general linear group and the theory of symplectic singularities, we study a category of perverse sheaves with coefficients in a field $k$ on any affine unimodular hypertoric variety.…

We propose a construction of a tensor exact category F_X^m of Artin-Tate motivic sheaves with finite coefficients Z/m over an algebraic variety X (over a field K of characteristic prime to m) in terms of etale sheaves of Z/m-modules over X.…

Let $S\to C$ be a smooth projective surface with numerically trivial canonical bundle fibered onto a curve. We prove the multiplicativity of the perverse filtration with respect to the cup product on $H^*(S^{[n]},\mathbb{Q})$ for the…

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…

This thesis deals with the general problem of determining when the heart $\mathcal{H}$ of a t-structure in a triangulated category $\mathcal{D}$ is a Grothendieck or a module category. As preliminaries, we study Grothendieck conditions…

We study when the heart of a t-structure in a triangulated category $\mathcal{D}$ with coproducts is AB5 or a Grothendieck category. If $\mathcal{D}$ satisfies Brown representability, a t-structure has an AB5 heart with an injective…

Let $\Delta$ be the Artin complex of the Artin group of type $D_n$. This complex is also called the spherical Deligne complex of type $D_n$. We show certain types of 6-cycles in the 1-skeleton of $\Delta$ either have a center, which is a…

For an arbitrary complex algebraic variety which is not necessarily pure dimensional, the intersection complex can be defined as the direct sum of the Deligne-Goresky-MacPherson intersection complexes of each irreducible component. We give…