A CHARACTERIZATION OF RATIONAL-SINGULARITIES IN TERMS OF INJECTIVITY OF FROBENIUS MAPS

Authors
Citation
N. Hara, A CHARACTERIZATION OF RATIONAL-SINGULARITIES IN TERMS OF INJECTIVITY OF FROBENIUS MAPS, American journal of mathematics, 120(5), 1998, pp. 981-996
Citations number
30
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics,Mathematics
ISSN journal
0002-9327
Volume
120
Issue
5
Year of publication
1998
Pages
981 - 996
Database
ISI
SICI code
0002-9327(1998)120:5<981:ACORIT>2.0.ZU;2-8
Abstract
The notions of F-rational and F-regular rings are defined via tight cl osure, which is a closure operation for ideals in a commutative ring o f positive characteristic. The geometric significance of these notions has persisted, and K. E. Smith proved that F-rational rings have rati onal singularities. We now ask about the converse implication. The ans wer to this question is yes and no. For a fixed positive characteristi c, there is a rational singularity which is not F-rational, so the ans wer is no. In this paper, however, we aim to show that the answer is y es in the following sense: If a ring of characteristic zero has ration al singularity, then its module p reduction is F-rational for almost a ll characteristic p. This result leads us to the correspondence of F-r egular rings and log terminal singularities.