TY - JOUR
T1 - A generalization of tight closure and multiplier ideals
AU - Hara, Nobuo
AU - Yoshida, Ken Ichi
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2003/8
Y1 - 2003/8
N2 - We introduce a new variant of tight closure associated to any fixed ideal a, which we call a-tight closure, and study various properties thereof. In our theory, the annihilator ideal τ(a) of all a-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 τ(a) and the multiplier ideal associated to a (or, the adjoint of a in Lipman's sense) in normal ℚ-Gorenstein rings reduced from characteristic zero to characteristic p ≫ 0. Also, in fixed prime characteristic, we establish some properties of τ(a) 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 τ(a) and the F-rationality of Rees algebras.
AB - We introduce a new variant of tight closure associated to any fixed ideal a, which we call a-tight closure, and study various properties thereof. In our theory, the annihilator ideal τ(a) of all a-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 τ(a) and the multiplier ideal associated to a (or, the adjoint of a in Lipman's sense) in normal ℚ-Gorenstein rings reduced from characteristic zero to characteristic p ≫ 0. Also, in fixed prime characteristic, we establish some properties of τ(a) 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 τ(a) and the F-rationality of Rees algebras.
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U2 - 10.1090/S0002-9947-03-03285-9
DO - 10.1090/S0002-9947-03-03285-9
M3 - Article
AN - SCOPUS:0043246626
VL - 355
SP - 3143
EP - 3174
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 8
ER -