Subcategories of singularity categories via tensor actions

TL;DR

This paper classifies localizing and thick subcategories of singularity categories for affine schemes with hypersurface singularities and local complete intersections using tensor actions, and relates these classifications to the telescope conjecture.

Contribution

It provides a complete classification of subcategories in singularity categories for specific algebraic schemes using tensor action formalism, linking to the telescope conjecture.

Findings

Classifies localizing subcategories of stable derived categories for hypersurface singularities.

Classifies thick subcategories of singularity categories for certain schemes.

Connects classifications to the (relative) telescope conjecture.

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.