Related papers: Artin perverse sheaves

Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…

Let T be a compact complex torus, dim T>2. We show that the category of coherent sheaves on T is independent of the choice of the complex structure, if this complex structure is generic. The proof is independent of math.AG/0205210, where…

In this note, we consider perverse sheaves on the nilpotent cone. We prove orthogonality relations for the equivariant category of sheaves on the nilpotent cone in a method similar to Lusztig's for character sheaves. We also consider…

First, we show that a compact object $C$ in a triangulated category, which satisfies suitable conditions, induces a $t$-structure. Second, in an abelian category we show that a complex $P^{\centerdot}$ of small projective objects of term…

Let T be a Hom-finite triangulated Krull-Schmidt category over a field k. Inspired by a definition of Koenig and Liu, we say that a family S of pairwise orthogonal objects in T with trivial endomorphism rings is a simple-minded system if…

Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $\mathcal{P}$ a separated smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $X$ a smooth closed subscheme of $P$, $T$ a divisor in $P$ such that…

We study the role of the Serre functor in the theory of derived equivalences. Let $\mathcal{A}$ be an abelian category and let $(\mathcal{U}, \mathcal{V})$ be a $t$-structure on the bounded derived category $D^b \mathcal{A}$ with heart…

The main goal of this paper is to establish close relations among sheaves of modules on atomic sites, representations of categories, and discrete representations of topological groups. We characterize sheaves of modules on atomic sites as…

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…

A graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty intersection. We show that weak Garside groups of finite type and FC-type Artin groups are Helly, that is, they act geometrically on Helly graphs.…

For a complex reductive Lie group G with Lie algebra g, Cartan subalgebra h and Weyl group W, we describe the category of perverse sheaves on h/W smooth w.r.t the natural stratification. The answer is given in terms of mixed Bruhat sheaves,…

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…

An \'etale homotopy type $T(X, z)$ associated to any pointed locally fibrant connected simplicial sheaf $(X, z)$ on a pointed locally connected small Grothendieck site $(\mc{C}, x)$ is studied. It is shown that this type $T(X, z)$…

We study a class of perverse sheaves on some spherical varieties which include the strata of the De Concini-Procesi completion of a symmetric variety. This is a generalization of the theory of (parabolic) character sheaves.

We study the equivariant cohomology of spherical perverse sheaves on the affine Grassmannian of a connected reductive group $G$ with support in the affine Grassmannian of any Levi subgroup $L$ of $G$. In doing so, we extend the work of…

Let $k$ be a field of characteristic $0$ endowed with a complex embedding $\sigma: k \hookrightarrow \mathbb{C}$. In this paper we complete the construction of the six functor formalism on perverse Nori motives over quasi-projective…

Given a complex manifold S, we introduce for each complex manifold X a t-structure on the bounded derived category of C-constructible complexes of O_S-modules on X x S. We prove that the de Rham complex of a holonomic D_{XxS/S}-module which…

We classify the simple integrable modules of double affine Hecke algebras via perverse sheaves. We get also some estimate for the Jordan-Holder multiplicities of induced modules.

To a smooth and proper morphism $\mathcal{X}\to U$ with quasicompact semiseparated target we associate a sheaf in the \'etale topology, which takes an affine $U$-scheme $V$ to the set of $V$-linear semiorthogonal decompositions (of fixed…

We study intersections of complex Lagrangian in complex symplectic manifolds, proving two main results. First, we construct global canonical perverse sheaves on complex Lagrangian intersections in complex symplectic manifolds for any pair…