F-regularity does not deform
نویسندگان
چکیده
منابع مشابه
F-regularity Does Not Deform
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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For a Noetherian local domain (R, m, K), it is an open question whether strong F–regularity deforms. We provide an affirmative answer to this question when the canonical module satisfies certain additional assumptions. The techniques used here involve passing to a Gorenstein ring, using an anti– canonical cover.
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 1999
ISSN: 1080-6377
DOI: 10.1353/ajm.1999.0029