Related papers: Lecture notes on sheaves and perverse sheaves

We study derived categories of coherent sheaves on abelian varieties. We give a criterion for the equivalence of the derived categories on two abelian varieties. We describe the autoequivalence group for the derived category of coherent…

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…

In this paper, we study deformations of nonsingular Poisson varieties, deformations of Poisson invertible sheaves and simultaneous deformations of nonsingular Poisson varieties and Poisson invertible sheaves, which extend flat deformation…

We introduce, on a topological space X, a class of stacks of abelian categories we call "stacks of type P." This class of stacks includes the stack of perverse sheaves (of any perversity, constructible with respect to a fixed…

We study a variation of Carlsson and Zomorodian's persistent homology. As an application, we analyze the persistent cellular sheaf cohomology of network coding sheaves on deteriorating networks.

We propose the notion of perverse coherent sheaves for symplectic singularities and study its properties. In particular, it gives a basis of simple objects in the Grothendieck group of Poisson sheaves. We show that perverse coherent bases…

These lecture notes were prepared for the workshop ``Algebraic Geometry: Presentations by Young Researchers'' in Snowbird, Utah, July 2004, and for the autumn school in Lukecin, Poland, September 2004. In six lectures I attempted to present…

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…

I present a quick overview of the current status of Chiral perturbation theory in the meson sector. To illustrate the successes and some problems in the description of the phenomenology, I focus on a few selected examples that are relevant…

We study sheaves in the context of a duality theory for lattice structure endowed with extra operations, and in the context of forcing in a topos. Using Sheaf duality theory of Comer for cylindric algebras, we give a representation theorem…

These lectures describe the use of effective field theories to extrapolate results from the parameter region where numerical simulations of lattice QCD are possible to the physical parameters (physical quark masses, infinite volume,…

We present the construction and properties of a self-dual perverse sheaf S_0 whose cohomology fulfills some of the requirements of String theory as outlined by T. Hubsch in hep-th/9612075. The construction of this S_0 utilizes techniques…

In the strict semi stable reduction situation, we describe the various filtrations of the perverse sheaf of nearby cycles in terms of irreducible perverse sheaves together with the action of the monodromy operator. We then study the…

In type theory, an oracle may be specified abstractly by a predicate whose domain is the type of queries asked of the oracle, and whose proofs are the oracle answers. Such a specification induces an oracle modality that captures a…

This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.

For a stratified topological space we introduce the category of IC-modules, which are linear algebra devices with the relations described by the equation d^2=0. We prove that the category of (mixed) IC-modules is equivalent to the category…

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…

These notes describe how perturbative on-shell and off-shell string amplitudes can be computed using string field theory. Computational methods for approximating arbitrary amplitudes are discussed, and compared with standard world-sheet…

The purpose of this paper is to introduce and study certain irreducible perverse l-adic sheaves on a reductive group G over a finite field (we call them gamma-sheaves). One can construct such a sheaf starting with (almost) every…

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…