Nagoya Mathematical Journal

Test ideals vs. multiplier ideals

Mircea Mustaţă and Ken-ichi Yoshida

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Abstract

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).

Article information

Source
Nagoya Math. J., Volume 193 (2009), 111-128.

Dates
First available in Project Euclid: 3 March 2009

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1236089983

Mathematical Reviews number (MathSciNet)
MR2502910

Zentralblatt MATH identifier
1162.13004

Subjects
Primary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]

Citation

Mustaţă, Mircea; Yoshida, Ken-ichi. Test ideals vs. multiplier ideals. Nagoya Math. J. 193 (2009), 111--128. https://projecteuclid.org/euclid.nmj/1236089983


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