Grothendieck Duality and Q-Gorenstein Morphisms.

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 Kollár condition, over a field. By studying the relative S2-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. [ABSTRACT FROM AUTHOR]