On modules of finite projective dimension over complete intersections

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)113-116
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - Jan 2003


  • Complete intersection
  • Finite projective dimension
  • Flatness
  • Frobenius
  • Tor

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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