Grothendieck duality and Q-Gorenstein morphisms

Abstract

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.

111 pages. This is the revised version of the preprint: RIMS-1861

Cited by in corpus (1)

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