Journal of the American Mathematical Society

Author(s): Holger Brenner; Mordechai Katzman
Journal: J. Amer. Math. Soc. 19 (2006), 659-672.
MSC (2000): Primary 13A35; Secondary 11A41, 14H60
Posted: December 22, 2005
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Abstract: We provide a negative answer to an old question in tight closure theory by showing that the containment $x^3y^3 \in (x^4,y^4,z^4)^*$ in $\mathbb{K}[x,y,z]/(x^7+y^7-z^7)$ holds for infinitely many but not for almost all prime characteristics of the field $\mathbb{K}$ . This proves that tight closure exhibits a strong dependence on the arithmetic of the prime characteristic. The ideal $(x,y,z) \subset \mathbb{K}[x,y,z,u,v,w]/(x^7+y^7-z^7, ux^4+vy^4+wz^4+x^3y^3)$ has then the property that the cohomological dimension fluctuates arithmetically between 0 and

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Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 13A35, 11A41, 14H60

Holger Brenner
Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email: H.Brenner@sheffield.ac.uk

Mordechai Katzman
Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email: M.Katzman@sheffield.ac.uk

DOI: 10.1090/S0894-0347-05-00514-X
PII: S 0894-0347(05)00514-X
Keywords: Tight closure, dependence on prime numbers, cohomological dimension, semistable bundles.
Received by editor(s): December 3, 2004
Posted: December 22, 2005
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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