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Grothendieck duality and Q-Gorenstein morphisms (1612.01690v1)
Published 6 Dec 2016 in math.AG
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 Koll\'ar 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.