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Test Ideals Vs. Multiplier Ideals

Published online by Cambridge University Press:  11 January 2016

Mircea Mustaţă and
Ken-Ichi Yoshida
Mircea Mustaţă
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA, mmustata@umich.edu
Ken-Ichi Yoshida
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan, yoshida@math.nagoya-u.ac.jp
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Abstract

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The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via vanishing theorems. In this note we give several examples to emphasize the different behavior of test ideals and multiplier ideals. Our main result is that every ideal in an F-finite regular local ring can be written as a generalized test ideal. We also prove the semicontinuity of F-pure thresholds (though the analogue of the Generic Restriction Theorem for multiplier ideals does not hold).

Keywords

13A3514B05

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 193 , 2009, pp. 111 - 128
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

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