Characterizations of regular local rings in positive characteristics
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Abstract:
In this note, we provide several characterizations of regular local rings in positive characteristics, in terms of the Hilbert-Kunz multiplicity and its higher $\mathrm {Tor}$ counterparts ${\mathfrak {i}} t_i={\lim }_{n \to \infty } \ell (\mathrm {Tor}_i(k,{}^{f^n}\!\! R))/p^{nd}$. We also apply the characterizations to improve a recent result by Bridgeland and Iyengar in the characteristic $p$ case. Our proof avoids using the existence of big Cohen-Macaulay modules, which is the major tool in the proof of Bridgeland and Iyengar.References
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Additional Information
- Jinjia Li
- Affiliation: Department of Mathematics, Syracuse University, 215 Carnegie, Syracuse, New York 13244
- Email: jli32@syr.edu
- Received by editor(s): December 1, 2006
- Received by editor(s) in revised form: February 19, 2007
- Published electronically: November 23, 2007
- Communicated by: Bernd Ulrich
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1553-1558
- MSC (2000): Primary 13A35, 13D07, 13D25, 13H05
- DOI: https://doi.org/10.1090/S0002-9939-07-09158-7
- MathSciNet review: 2373583