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.

中文翻译：

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任意方案派生类别的不可分解性

我们将 Kawatani 和 Okawa 的标准扩展到任意方案的光滑投影簇的派生类别的不可分解性。对于相关方案，我们还给出了不存在基上线性的半正交分解的准则。这些标准基于全局或​​相对二元化复合体的基本基因座。