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Induced formal deformations and the Cohen-Macaulay property


Author: Phillip Griffith
Journal: Trans. Amer. Math. Soc. 353 (2001), 77-93
MSC (2000): Primary 13B10, 13B15, 13D10, 13F40; Secondary 13H10, 13N05, 14B07
DOI: https://doi.org/10.1090/S0002-9947-00-02513-7
Published electronically: June 13, 2000
MathSciNet review: 1675194
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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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Additional Information

Phillip Griffith
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email: griffith@math.uiuc.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02513-7
Keywords: Cohen-Macaulay local rings, normal domains, ramification, deformations, Segre products.
Received by editor(s): August 15, 1998
Published electronically: June 13, 2000
Additional Notes: The author would like to thank the referee for several corrections and helpful suggestions.
$^{*}$ See Added in Proof for correction
Article copyright: © Copyright 2000 American Mathematical Society

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