Subcategories of singularity categories via tensor actions

Details Subcategories of singularity categories via tensor actions Subcategories of singularity categories via tensor actions

2011-05-24

arxiv.org/abs/1105.4698v2

Mathematics

Algebraic Geometry

43 pages, comments welcome; reformatted, minor corrections, main result improved

Scientific paper

We obtain, via the formalism of tensor actions, a complete classification of the localizing subcategories of the stable derived category of any affine scheme with hypersurface singularities and of any local complete intersection over a field; 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.

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