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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Characterization of modules of finite projective dimension over complete intersections


Author: Jinjia Li
Journal: Proc. Amer. Math. Soc. 134 (2006), 1271-1275
MSC (2000): Primary 13C14, 13C40, 13D05, 13D40, 13H10
Published electronically: October 13, 2005
MathSciNet review: 2199169
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ M$ be a finitely generated module over a local complete intersection $ R$ of characteristic $ p>0$. The property that $ M$ has finite projective dimension can be characterized by the vanishing of $ \operatorname{ext}_R^i({}^{f^n} R,M)$ for some $ i>0$ and for some $ n>0$.


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Additional Information

Jinjia Li
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: jinjiali@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08174-8
PII: S 0002-9939(05)08174-8
Keywords: Complete intersection, finite projective dimension, finite injective dimension, flatness, Frobenius, Ext, Tor
Received by editor(s): October 4, 2004
Received by editor(s) in revised form: December 14, 2004
Published electronically: October 13, 2005
Additional Notes: This research was carried out while the author was supported by a research grant from the UIUC Campus Research Board of the University of Illinois under the supervision of S. Dutta
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.