Indecomposability of derived categories for arbitrary schemes

TL;DR

This paper generalizes criteria for the indecomposability of derived categories from smooth projective varieties to arbitrary schemes, providing tools to analyze their structure and semiorthogonal decompositions.

Contribution

It extends the indecomposability criterion to all schemes and introduces a criterion for the nonexistence of certain semiorthogonal decompositions based on dualizing complexes.

Findings

Criteria for indecomposability of derived categories for arbitrary schemes

Conditions for the nonexistence of semiorthogonal decompositions

Use of base loci of dualizing complexes in these criteria

Abstract

We extend the criterion of Kawatani and Okawa for indecomposability of the derived category of a smooth projective variety to arbitrary schemes. For relative schemes, we also give a criterion for the nonexistence of semiorthogonal decompositions that are linear over the base. These criteria are based on the base loci of the global or relative dualizing complexes.