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

 

On modules of finite projective dimension over complete intersections


Author: S. P. Dutta
Journal: Proc. Amer. Math. Soc. 131 (2003), 113-116
MSC (2000): Primary 13C14, 13C40, 13D05, 13D40, 13H10
Published electronically: May 22, 2002
MathSciNet review: 1929030
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Abstract: Recently Avramov and Miller proved that over a local complete intersection ring $(R,m,k)$ in characteristic $p>0$, a finitely generated module $M$ has finite projective dimension if for some $i>0$ and for some $n>0$, $\operatorname{Tor}^{R}_{i}(M,f^{n}_{R})=0-f^{n}$ being the frobenius map repeated $n$ times. They used the notion of ``complexity'' and several related theorems. Here we offer a very simple proof of the above theorem without using ``complexity'' at all.


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Additional Information

S. P. Dutta
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email: dutta@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06536-X
PII: S 0002-9939(02)06536-X
Keywords: Complete intersection, finite projective dimension, flatness, Frobenius, Tor
Received by editor(s): June 18, 2001
Received by editor(s) in revised form: September 3, 2001
Published electronically: May 22, 2002
Additional Notes: This research was partially supported by an NSF grant
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2002 American Mathematical Society