A generalization of the Auslander-Nagata purity theorem

Kantorovitz, Miriam

doi:10.1090/S0002-9939-99-04501-3

A generalization of the Auslander-Nagata purity theorem
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by Miriam Ruth Kantorovitz

Proc. Amer. Math. Soc. 127 (1999), 71-78

DOI: https://doi.org/10.1090/S0002-9939-99-04501-3

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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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