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Published online: 2018-07-23
Grothendieck Duality and $\mathbb Q$-Gorenstein MorphismsYongnam Lee and Noboru Nakayama (1) Korea Advanced Institute of Science and Technology, Daejeon, South Korea
(2) Kyoto University, Japan
The notions of a $\mathbb Q$-Gorenstein scheme and a $\mathbb Q$-Gorenstein morphism are introduced for locally Noetherian schemes by dualizing complexes and (relative) canonical sheaves. These cover all the previously known notions of a $\mathbb Q$-Gorenstein algebraic variety and a $\mathbb Q$-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 $\mathbb Q$-Gorenstein morphisms, which include the infinitesimal criteria, the valuative criterion, and $\mathbb Q$-Gorenstein refinements.
Keywords: Grothendieck duality, $\mathbb Q$-Gorenstein morphism
Lee Yongnam, Nakayama Noboru: Grothendieck Duality and $\mathbb Q$-Gorenstein Morphisms. Publ. Res. Inst. Math. Sci. 54 (2018), 517-648. doi: 10.4171/PRIMS/54-3-3