Duality for bounded derived categories of complete intersections

TL;DR

This paper demonstrates that all thick subcategories of the singularity and bounded derived categories of complete intersection rings are self-dual, revealing symmetry properties in their structure and cohomology vanishing behaviors.

Contribution

It establishes the self-duality of thick subcategories in singularity and bounded derived categories for complete intersections, extending to certain schemes and highlighting symmetry in cohomology.

Findings

Thick subcategories are self-dual in these categories.

Results apply to complete intersection schemes.

Implications for symmetry in cohomology vanishing.

Abstract

We show that every thick subcategory of the singularity category of a complete intersection ring is self dual. We also prove the analogous statement for thick subcategories of the bounded derived category and give applications to the symmetry of vanishing of cohomology. These results are also proved for certain complete intersection schemes.