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Subcategories of singularity categories via tensor actions

Published online by Cambridge University Press:  22 November 2013

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.

Type
Research Article
Copyright
© The Author(s) 2013 

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