Phantom depth and flat base change
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- by Neil M. Epstein PDF
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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.References
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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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2175997