論文

査読有り
2003年

A generalization of tight closure and multiplier ideals

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
  • N Hara
  • ,
  • K Yoshida

355
8
開始ページ
3143
終了ページ
3174
記述言語
英語
掲載種別
研究論文(学術雑誌)
出版者・発行元
AMER MATHEMATICAL SOC

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 tau(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 tau(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 tau(a) similar to those of multiplier ideals (e. g., a Briancon-Skoda-type theorem, subadditivity, etc.) with considerably simple proofs, and study the relationship between the ideal tau(a) and the F-rationality of Rees algebras.

Web of Science ® 被引用回数 : 108

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Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000182986900007&DestApp=WOS_CPL

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