A generalization of tight closure and multiplier ideals

Authors:
Nobuo Hara and Ken-ichi Yoshida

Journal:
Trans. Amer. Math. Soc. **355** (2003), 3143-3174

MSC (2000):
Primary 13A35, 14B05

DOI:
https://doi.org/10.1090/S0002-9947-03-03285-9

Published electronically:
April 11, 2003

MathSciNet review:
1974679

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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a new variant of tight closure associated to any fixed ideal , which we call -tight closure, and study various properties thereof. In our theory, the annihilator ideal of all -tight closure relations, which is a generalization of the test ideal in the usual tight closure theory, plays a particularly important role. We prove the correspondence of the ideal and the multiplier ideal associated to (or, the adjoint of in Lipman's sense) in normal -Gorenstein rings reduced from characteristic zero to characteristic . Also, in fixed prime characteristic, we establish some properties of similar to those of multiplier ideals (e.g., a Briançon-Skoda-type theorem, subadditivity, etc.) with considerably simple proofs, and study the relationship between the ideal and the F-rationality of Rees algebras.

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Additional Information

**Nobuo Hara**

Affiliation:
Mathematical Institute, Tohoku University, Sendai 980–8578, Japan

Email:
hara@math.tohoku.ac.jp

**Ken-ichi Yoshida**

Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464–8602, Japan

Email:
yoshida@math.nagoya-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-03-03285-9

Received by editor(s):
August 20, 2002

Received by editor(s) in revised form:
December 19, 2002

Published electronically:
April 11, 2003

Additional Notes:
Both authors are partially supported by a Grant-in-Aid for Scientific Research, Japan

Article copyright:
© Copyright 2003
American Mathematical Society