Oct, 1998
A characterization of rational singularities in terms of injectivity of Frobenius maps
AMERICAN JOURNAL OF MATHEMATICS
- Volume
- 120
- Number
- 5
- First page
- 981
- Last page
- 996
- Language
- English
- Publishing type
- Research paper (scientific journal)
- Publisher
- 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.
- Link information
- ID information
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- ISSN : 0002-9327
- Web of Science ID : WOS:000076236400004