Duality for bounded derived categories of complete intersections

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. In order to prove these results for the bounded derived category, we extend the classification of thick subcategories for the singularity category to the whole bounded derived category. These results are also proved for certain complete intersection schemes.