Grothendieck Duality and Q-Gorenstein Morphisms

Abstract

The notions of a Q-Gorenstein scheme and a Q-Gorenstein morphism are introduced for locally Noetherian schemes by dualizing complexes and (relative) canonical sheaves. These cover all the previously known notions of a Q-Gorenstein algebraic variety and a Q-Gorenstein deformation satisfying the Kollar condition, over a field. By studying the relative S-2-condition and base change properties, valuable results are proved for Q-Gorenstein morphisms, which include the infinitesimal criteria, the valuative criterion, and Q-Gorenstein refinements.