Publications of the Research Institute for Mathematical Sciences


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Volume 54, Issue 3, 2018, pp. 517–648
DOI: 10.4171/PRIMS/54-3-3

Published online: 2018-07-23

Grothendieck Duality and $\mathbb Q$-Gorenstein Morphisms

Yongnam Lee[1] and Noboru Nakayama[2]

(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 fi eld. By studying the relative S$_2$-condition and base change properties, valuable results are proved for $\mathbb Q$-Gorenstein morphisms, which include the in finitesimal criteria, the valuative criterion, and $\mathbb Q$-Gorenstein re finements.

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