Transactions of the American Mathematical Society

Author(s): Phillip Griffith
Journal: Trans. Amer. Math. Soc. 353 (2001), 77-93.
MSC (2000): Primary 13B10, 13B15, 13D10, 13F40; Secondary 13H10, 13N05, 14B07
Posted: June 13, 2000
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Abstract: The main result states: if

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

, then there is a corresponding

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

DOI: 10.1090/S0002-9947-00-02513-7
PII: S 0002-9947(00)02513-7
Keywords: Cohen-Macaulay local rings, normal domains, ramification, deformations, Segre products.
Received by editor(s): August 15, 1998
Posted: 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
Copyright of article: Copyright 2000, American Mathematical Society

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