Induced formal deformations and the Cohen-Macaulay property

Griffith, Phillip

doi:10.1090/S0002-9947-00-02513-7

Induced formal deformations and the Cohen-Macaulay property
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by Phillip Griffith

Trans. Amer. Math. Soc. 353 (2001), 77-93

DOI: https://doi.org/10.1090/S0002-9947-00-02513-7

Published electronically: June 13, 2000

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Abstract:

The main result states: if $A/B$ is a module finite extension of excellent local normal domains which is unramified in codimension two and if $S/\varkappa S \simeq \hat B$ represents a deformation of the completion of $B$, then there is a corresponding $S$-algebra deformation $T/\varkappa T \simeq \hat A$ such that the ring homomorphism $S \hookrightarrow T$ represents a deformation of $\hat B \hookrightarrow \hat A$. The main application is to the ascent of the arithmetic Cohen-Macaulay property for an étale map $f : X \to Y$ of smooth projective varieties over an algebraically closed field.${}^*$

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