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A generalization of the Auslander-Nagata purity theorem

Author(s): Miriam Ruth Kantorovitz
Journal: Proc. Amer. Math. Soc. 127 (1999), 71-78.
MSC (1991): Primary 13B15; Secondary 13B02
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Abstract: Let $B \hookrightarrow A$ be a module finite extension of normal domains. We show that if $B \hookrightarrow A$ is unramified in codimension one and if $A$ has finite projective dimension over $B$, then $A$ is étale over $B$. Our proof makes use of P. Roberts' New Intersection Theorem.

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Additional Information:

Miriam Ruth Kantorovitz
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: ruth@math.uiuc.edu

DOI: 10.1090/S0002-9939-99-04501-3
PII: S 0002-9939(99)04501-3
Keywords: Auslander-Nagata purity, unramified extension
Received by editor(s): October 17, 1996
Received by editor(s) in revised form: May 14, 1997
Communicated by: Wolmer V. Vasconcelos
Copyright of article: Copyright 1999, American Mathematical Society

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