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Koszul Duality Patterns in Representation Theory
The aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of Koszul duality to repre- sentation theory. The paper consists of three partsExpand
A proof of Jantzen conjectures
On the derived category of perverse sheaves
Let D : Db(x, ~ ) be the usual derived category of ~-sheaves on a certain scheme X, and M = M{X)c D be the category of perverse sheaves for middle perversity. Now consider the derived category Db(M)Expand
Determinant bundles and Virasoro algebras
We consider the interplay of infinite-dimensional Lie algebras of Virasoro type and moduli spaces of curves, suggested by string theory. We will see that the infinitesimal geometry of determinantExpand
How to glue perverse sheaves
The aim of this note [0] is to give a short, self-contained account of the vanishing cycle constructions of perverse sheaves; e.g., for the needs of [1]. It differs somewhat from the alternativeExpand
Tilting exercises
We discuss tilting objects in categories of perverse sheaves smooth along some stratification. In case of the Schubert stratification we show that the Radon transform interchanges tilting,Expand
Constructible sheaves are holonomic
We develop the theory of singular support for étale sheaves on algebraic varieties over an arbitrary base field.