Indecomposability of derived categories for arbitrary schemes

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