論文

査読有り
1998年10月

A characterization of rational singularities in terms of injectivity of Frobenius maps

AMERICAN JOURNAL OF MATHEMATICS
  • N Hara

120
5
開始ページ
981
終了ページ
996
記述言語
英語
掲載種別
研究論文(学術雑誌)
出版者・発行元
JOHNS HOPKINS UNIV PRESS

The notions of F-rational and F-regular rings are defined via tight closure, which is a closure operation for ideals in a commutative ring of positive characteristic. The geometric significance of these notions has persisted, and K. E. Smith proved that F-rational rings have rational singularities. We now ask about the converse implication. The answer to this question is yes and no. For a fixed positive characteristic, there is a rational singularity which is not F-rational, so the answer is no. In this paper, however, we aim to show that the answer is yes in the following sense: If a ring of characteristic zero has rational singularity, then its module p reduction is F-rational for almost all characteristic p. This result leads us to the correspondence of F-regular rings and log terminal singularities.

Web of Science ® 被引用回数 : 93

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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:000076236400004&DestApp=WOS_CPL

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