Abstract.
Let M be a module of finite length over a complete intersection (R,m) of characteristic \(p>0\). We characterize the property that M has finite projective dimension in terms of the asymptotic behavior of a certain length function defined using the Frobenius functor. This may be viewed as the converse to a theorem of S. Dutta. As a corollary we get that, in a complete intersection (R,m), an m-primary ideal I has finite projective dimension if and only if its Hilbert-Kunz multiplicity equals the length of R/I.
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Received June 22, 1998; in final form October 13, 1998
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Miller, C. A Frobenius characterization of finite projective dimension over complete intersections. Math Z 233, 127–136 (2000). https://doi.org/10.1007/PL00004783
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DOI: https://doi.org/10.1007/PL00004783