Phantom depth and flat base change
Author:
Neil M. Epstein
Journal:
Proc. Amer. Math. Soc. 134 (2006), 313-321
MSC (2000):
Primary 13A35; Secondary 13B40, 13C15, 13H10
DOI:
https://doi.org/10.1090/S0002-9939-05-08223-7
Published electronically:
September 21, 2005
MathSciNet review:
2175997
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We prove that if $f: (R,\mathfrak {m}) \rightarrow (S,\mathfrak {n})$ is a flat local homomorphism, $S/\mathfrak {m} S$ is Cohen-Macaulay and $F$-injective, and $R$ and $S$ share a weak test element, then a tight closure analogue of the (standard) formula for depth and regular sequences across flat base change holds. As a corollary, it follows that phantom depth commutes with completion for excellent local rings. We give examples to show that the analogue does not hold for surjective base change.
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Additional Information
Neil M. Epstein
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Address at time of publication:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
MR Author ID:
768826
Email:
epstein@math.ku.edu, neilme@umich.edu
Keywords:
Tight closure,
phantom depth,
base change
Received by editor(s):
May 17, 2004
Published electronically:
September 21, 2005
Additional Notes:
The author was partially supported by the National Science Foundation.
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
