Subcategories of singularity categories via tensor actions
Algebraic Geometry
2014-03-19 v3 Commutative Algebra
Category Theory
Abstract
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.
Cite
@article{arxiv.1105.4698,
title = {Subcategories of singularity categories via tensor actions},
author = {Greg Stevenson},
journal= {arXiv preprint arXiv:1105.4698},
year = {2014}
}
Comments
43 pages, comments welcome; references to the paper on tensor actions updated