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Subcategories of singularity categories via tensor actions

Part of: Abelian categories Special varieties (Co)homology theory

Published online by Cambridge University Press:  22 November 2013

Greg Stevenson
Greg Stevenson*
Affiliation:
Universität Bielefeld, Fakultät für Mathematik, BIREP Gruppe, Postfach 10 01 31, 33501 Bielefeld, Germany email gstevens@math.uni-bielefeld.de
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Abstract

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We obtain, via the formalism of tensor actions, a complete classification of the localizing subcategories of the stable derived category of any affine scheme that has hypersurface singularities or is a complete intersection in a regular scheme; in particular, this classifies the thick subcategories of the singularity categories of such rings. The analogous result is also proved for certain locally complete intersection schemes. It is also shown that from each of these classifications one can deduce the (relative) telescope conjecture.

Keywords

singularity categorycomplete intersectionlocalizing subcategorytriangular geometrytelescope conjecture

MSC classification

Secondary: 14M10: Complete intersections 18E30: Derived categories, triangulated categories 14F05: Sheaves, derived categories of sheaves and related constructions
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 2 , February 2014 , pp. 229 - 272
Copyright
© The Author(s) 2013 

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