Twisted sheaves and the period-index problem
نویسندگان
چکیده
منابع مشابه
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...
متن کاملModuli of Twisted Orbifold Sheaves and the Period-index Problem
We prove that certain stacks of slope-semistable twisted sheaves on orbisurfaces are non-empty and geometrically irreducible. Using these results, we prove the standard period-index conjecture for Brauer classes over function fields of surfaces over finite fields.
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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...
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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.
متن کاملOn 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 ...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2008
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x07003144