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The vanishing of  implies that  is regular
Author(s):
Ian
M.
Aberbach
Journal:
Proc. Amer. Math. Soc.
133
(2005),
27-29.
MSC (2000):
Primary 13A35;
Secondary 13H05
Posted:
June 23, 2004
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Abstract:
Let  be an excellent local ring of positive prime characteristic. We show that if  , then  is regular. This improves a result of Schoutens, in which the additional hypothesis that  was an isolated singularity was required for the proof.
References:
-
- 1.
- I. M. Aberbach and F. Enescu, The structure of
 -pure rings, preprint, 2003. - 2.
- M. Hochster, Cyclic purity versus purity in excellent Noetherian rings, Trans. Amer. Math. Soc. 231 (1977), no. 2, 463-488. MR 57:3111
- 3.
- M. Hochster and C. Huneke, Infinite integral extensions and big Cohen-Macaulay algebras, Ann. of Math. (2) 135 (1992), no. 1, 53-89. MR 92m:13023
- 4.
- M. Hochster and C. Huneke,
 -regularity, test elements, and smooth base change, Trans. Amer. Math. Soc. 346 (1994), no. 1, 1-62. MR 95d:13007 - 5.
- Craig Huneke, Tight closure and its applications, With an appendix by Melvin Hochster. CBMS Regional Conference Series in Mathematics, 88. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1996. x+137 pp. ISBN: 0-8218-0412-X. MR 96m:13001
- 6.
- E. Kunz, Characterizations of regular local rings for characteristic
 , Amer. J. Math. 91 (1969), 772-784. MR 40:5609 - 7.
- E. Kunz, On Noetherian rings of characteristic
 ., Amer. J. Math. 98 (1976), no. 4, 999-1013. MR 55:5612 - 8.
- H. Schoutens, On the vanishing of Tor for the absolute integral closure, J. Algebra 275 (2004), 567-574.
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Additional Information:
Ian
M.
Aberbach
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email:
aberbach@math.missouri.edu
DOI:
10.1090/S0002-9939-04-07491-X
PII:
S 0002-9939(04)07491-X
Keywords:
Regular rings,
characteristic $p$,
absolute integral closure
Received by editor(s):
July 15, 2003
Received by editor(s) in revised form:
September 18, 2003
Posted:
June 23, 2004
Additional Notes:
The author was partially supported by the National Security Agency. He also wishes to thank the referee for a careful reading of this paper and several corrections.
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2004,
American Mathematical Society
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