Twisted Whittaker model and factorizable sheaves

Moduli of Twisted Sheaves

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to spaces of semistable vector bundles. In the case of surfaces, we show (under a mild hypothesis on the twisting class) that the spaces are asympotically geometric...

Moduli of Twisted Orbifold Sheaves

We study stacks of slope-semistable twisted sheaves on orbisurfaces with projective coarse spaces and prove that in certain cases they have many of the asymptotic properties enjoyed by the moduli of slope-semistable sheaves on smooth projective surfaces.

Twisted Whittaker models for metaplectic groups

Twisted sheaves and the period-index problem

We use twisted sheaves and their moduli spaces to study the Brauer group of a scheme. In particular, we (1) show how twisted methods can be efficiently used to re-prove the basic facts about the Brauer group and cohomological Brauer group (including Gabber’s theorem that they coincide for a separated union of two affine schemes), (2) give a new proof of de Jong’s periodindex theorem for surface...

On the Ubiquity of Twisted Sheaves

In this paper we describe several results, built up over the last decade or so, that use twisted sheaves to study questions in algebra, arithmetic, and cohomology. The paper is for the most part expository and aims to collect in one place what is known about these methods, their applications, and some questions about their future. It also hopes to be a guide to a chunk of the literature, where ...