Indecomposability of derived categories for arbitrary schemes

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.

Final version with an appendix by Shinnosuke Okawa. To appear in Collectanea Mathematica