, Volume 130, Issue 4, pp 425-431,
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Characterization of modules of finite projective dimension via Frobenius functors

Abstract

Let M be a finitely generated module over a local ring R of characteristic p > 0. If depth(R) = s, then the property that M has finite projective dimension can be characterized by the vanishing of the functor ${{\rm Ext}^i_R(M, ^{f^n}R)}$ for s + 1 consecutive values i > 0 and for infinitely many n. In addition, if R is a d-dimensional complete intersection, then M has finite projective dimension can be characterized by the vanishing of the functor ${{\rm Ext}^i_R(M, ^{f^n}R)}$ for some i ≥ d and some n > 0.