Subcategories of singularity categories via tensor actions

By Greg Stevenson. Compositio Mathematica, 2011

88 citations recorded by the source corpus.

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 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f85b214b563c616bb298e29dbcbb2b564b84b667

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The radius of a subcategory of modules (2011, background): “According to a recent preprint by Stevenson [21] (see also [16]), if R is a quotient of a regular local ring by a regular sequence, then one can classify the thick subcategories of CM(R) in terms of “support varieties”.”
Classification of resolving subcategories and grade consistent functions (2012, background): “of perfect complexes over R. The Hopkins-Neeman theorem was extended to schemes by Thomason [33] and recently to group algebras by Benson, Iyengar and Krause [10]. For many other similar results, see [8, 24, 27, 29, 31] and the references therein. Generally speaking, the less restrictive conditions ”
Support theory via actions of tensor triangulated categories (2011, background): “The details of this application can be found in [39].”
Singular support of coherent sheaves and the geometric Langlands conjecture (2012, methodology): “in Ho(IndCoh(Z)/QCoh(Z)) correspond to specialization-closed subsets. Under this correspondence, the category Ho(IndCohY (Z)/QCoh(Z)) corresponds to the subset Y ′⊂H′. (This is almost obvious because [Ste] uses Orlov’sequivalence of Theorem H.2.3 to study IndCoh(Z)/QCoh(Z).) To summarize, wecan also”