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1 results

  • Subcategories of singularity categories via tensor actions

  • Part of
  • Greg Stevenson
  • Journal:
    Compositio Mathematica / Volume 150 / Issue 2 / February 2014
    Published online by Cambridge University Press:
    22 November 2013, pp. 229-272
    Print publication:
    February 2014

  • 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.