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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Induced formal deformations and the Cohen-Macaulay property
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by Phillip Griffith PDF
Trans. Amer. Math. Soc. 353 (2001), 77-93 Request permission

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
  • 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
  • © Copyright 2000 American Mathematical Society
  • 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
  • MathSciNet review: 1675194