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F-regularity does not deform
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 121, Number 4, August 1999
- pp. 919-929
- 10.1353/ajm.1999.0029
- Article
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Abstract
We show that the property of F-regularity does not deform, and thereby settle a longstanding open question in the theory of tight closure. Specifically, we construct a three dimensional N-graded domain R which is not F-regular (or even F-pure), but has a quotient R/tR which is F-regular. Examples are constructed over fields of characteristic p > 0, as well as over fields of characteristic zero.
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