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

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Abstract: We prove that if is a flat local homomorphism, is Cohen-Macaulay and -injective, and and 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

Email:
epstein@math.ku.edu, neilme@umich.edu

DOI:
https://doi.org/10.1090/S0002-9939-05-08223-7

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.