Related papers: The Riemann-Hilbert Correspondence for Algebraic S…

Kazhdan and Lusztig identified the affine Hecke algebra $\mathcal{H}$ with an equivariant $K$-group of the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, i.e., the local Langlands parametrization of…

In this paper we prove first a general theorem on semiorthogonal decompositions in derived categories of coherent sheaves for flat families over a smooth base. Based on the results of math.AG/0510670, we then show that the derived…

We give an alternate formulation of pseudo-coherence over an arbitrary derived stack X. The full subcategory of pseudo-coherent objects forms a stable sub-infinity-category of the derived category associated to X. Using relative…

The geometric phase that appears in the effects of Aharonov-Bohm type is interpreted in the frame of Deligne's version of the Riemann-Hilbert correspondence. We extend also the concept of flat gauge field to $B$-branes which are coherent…

Graded Hecke algebras can be constructed geometrically, with constructible sheaves and equivariant cohomology. The input consists of a complex reductive group G (possibly disconnected) and a cuspidal local system on a nilpotent orbit for a…

We describe the derived category of coherent sheaves on the minimal resolution of the Kleinian singularity associated to a finite subgroup G of SL(2). Then, we give an application to the Euler-characteristic version of the Hall algebra of…

Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra…

For a finite quiver without sources or sinks, we prove that the homotopy category of acyclic complexes of injective modules over the corresponding finite dimensional algebra with radical square zero is triangle equivalent to the derived…

We remove the global quotient presentation input in the theory of windows in derived categories of smooth Artin stacks of finite type. As an application, we use existing results on flipping of strata for wall-crossing of Gieseker…

This paper studies the intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$ -elliptic sheaves in the higher-rank setting, where $\mathcal{D}$ is a "maximal order" in a central division algebra $D$ over a global…

In this paper, we construct derived equivalences between matrix subrings. As applications, we calculate the global dimensions and the finitistic dimensions of some matrix subrings. And we show that the finitistic dimension conjecture holds…

Let G be a complex algebraic semi-simple adjoint group and X a smooth complete symmetric G-variety. Let L_i be the irreducible G-equivariant intersection cohomology complexes on X, and L the direct sum of the L_i. Let E= Ext(L,L) be the…

On a compact connected Riemann surface $C$ of genus at least $2$, we construct Lagrangian correspondences between moduli spaces of rank-$n$ Higgs bundles (respectively, holomorphic connections) and the Hilbert schemes of points on $T^\ast…

We show how derived categories build bridges across the current mathematical mainstream, linking geometric and algebraic, commutative and noncommutative, local and global banks. Arches in these bridges are pieces of semiorthogonal…

We classify finite dimensional division real associative $\mathcal{Z}_2$-algebras, introduce composition $\mathcal{Z}_2$-algebras, and extend the Campbell-Baker-Hausdorff series and Lie correspondence in the context of linear Hu-Liu Leibniz…

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…

We discuss derived categories of coherent sheaves on algebraic varieties. We focus on the case of non-singular Calabi-Yau varieties and consider two unsolved problems: proving that birational varieties have equivalent derived categories,…

The Langlands correspondence for complex curves is traditionally formulated in terms of sheaves rather than functions. Recently, Langlands asked whether it is possible to construct a function-theoretic version. In this paper we use the…

We present a construction of autoequivalences of derived categories of symmetric algebras based on projective modules with periodic endomorphism algebras. This construction generalises autoequivalences previously constructed by…

We generalize the higher Riemann-Hilbert correspondence in the presence of scalar curvature for a (possibly non-compact) smooth manifold $M$. We show that the dg-category of curved $\infty$-local systems, the dg-category of graded vector…