On modules of finite projective dimension over complete intersections
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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.References
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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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 113-116
- MSC (2000): Primary 13C14, 13C40, 13D05, 13D40, 13H10
- DOI: https://doi.org/10.1090/S0002-9939-02-06536-X
- MathSciNet review: 1929030