Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ F$-thresholds of hypersurfaces


Authors: Manuel Blickle, Mircea Mustata and Karen E. Smith
Journal: Trans. Amer. Math. Soc. 361 (2009), 6549-6565
MSC (2000): Primary 13A35; Secondary 14B05
Published electronically: July 16, 2009
MathSciNet review: 2538604
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We use the $ D$-module theoretic description of generalized test ideals to show that in any $ F$-finite regular ring the $ F$-thresholds of hypersurfaces are discrete and rational. Furthermore we show that any limit of $ F$-pure thresholds of principal ideals in bounded dimension is again an $ F$-pure threshold; hence in particular the limit is rational.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 13A35, 14B05

Retrieve articles in all journals with MSC (2000): 13A35, 14B05


Additional Information

Manuel Blickle
Affiliation: Fachbereich Mathematik, Universität Duisburg-Essen, Standort Essen, 45117 Essen, Germany
Email: manuel.blickle@uni-essen.de

Mircea Mustata
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: mmustata@umich.edu

Karen E. Smith
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: kesmith@umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04719-9
PII: S 0002-9947(09)04719-9
Keywords: $F$-thresholds, test ideals, $F$-modules, nonstandard extension
Received by editor(s): July 23, 2007
Received by editor(s) in revised form: January 2, 2008
Published electronically: July 16, 2009
Additional Notes: Partial support was provided by grant SFB/TR 45 of the DFG (first author), NSF grants DMS-0758454, DMS 0111298 and a Packard Fellowship (second author), and NSF grant DMS-0500823(third author)
Article copyright: © Copyright 2009 American Mathematical Society