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 -thresholds of hypersurfaces
Author(s):
Manuel
Blickle;
Mircea
Mustata;
Karen
E.
Smith
Journal:
Trans. Amer. Math. Soc.
361
(2009),
6549-6565.
MSC (2000):
Primary 13A35;
Secondary 14B05
Posted:
July 16, 2009
MathSciNet review:
2538604
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Abstract:
We use the  -module theoretic description of generalized test ideals to show that in any  -finite regular ring the  -thresholds of hypersurfaces are discrete and rational. Furthermore we show that any limit of  -pure thresholds of principal ideals in bounded dimension is again an  -pure threshold; hence in particular the limit is rational.
References:
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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:
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
Posted:
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)
Copyright of article:
Copyright
2009,
American Mathematical Society
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