Brenner, H. and Katzman, M. (2004) On the arithmetic of tight closure. Journal of the American Mathematical Society, 19 (3). pp. 659-672. ISSN 0894-0347
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 K[x,y,z]/(x^7+y^7-z^7) holds for infinitely many but not for almost all prime characteristics of the field K. This proves that tight closure exhibits a strong dependence on the arithmetic of the prime characteristic. The ideal (x,y,z) \subset 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 1.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2006 American Mathematical Society. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | tight closure; dependence on prime numbers; cohomological dimension; semistable bundles |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Miss Anthea Tucker |
Date Deposited: | 18 Nov 2009 15:46 |
Last Modified: | 16 Nov 2015 16:12 |
Published Version: | http://www.ams.org/jams/2006-19-03/S0894-0347-05-0... |
Status: | Published |
Publisher: | American Mathematical Society |
Refereed: | Yes |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:10170 |