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, ToriR(M, fRn) = 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) |
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Pages (from-to) | 113-116 |
Number of pages | 4 |
Journal | Proceedings of the American Mathematical Society |
Volume | 131 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2003 |
Keywords
- Complete intersection
- Finite projective dimension
- Flatness
- Frobenius
- Tor
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics