Grothendieck duality and Q-Gorenstein morphisms

The notions of $\mathbb Q$-Gorenstein scheme and of $\mathbb Q$-Gorenstein morphism are introduced for locally Noetherian schemes by dualizing complexes and (relative) canonical sheaves. These cover all the previously known notions of $\mathbb Q$-Gorenstein algebraic variety and of $\mathbb Q$-Gorenstein deformation satisfying Kollár condition, over a field. By studies on relative $\mathbf S_{2}$-condition and base change properties, valuable results are proved for $\mathbb Q$-Gorenstein morphisms, which include infinitesimal criterion, valuative criterion, $\mathbb Q$-Gorenstein refinement, and so forth.

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