On modules of finite projective dimension over complete intersections

S. P. Dutta

doi:10.1090/S0002-9939-02-06536-X

On modules of finite projective dimension over complete intersections

S. P. Dutta

Mathematics

Research output: Contribution to journal › Article › peer-review

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, Tor_i^R(M, f_Rⁿ) = 0 - fⁿ 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.

Original language	English (US)
Pages (from-to)	113-116
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-02-06536-X
State	Published - Jan 2003

Keywords

Complete intersection
Finite projective dimension
Flatness
Frobenius
Tor

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-02-06536-X

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KW - Flatness

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On modules of finite projective dimension over complete intersections

Abstract

Keywords

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