A Frobenius characterization of finite projective dimension over complete intersections

Let M be a module of finite length over a complete intersection ( R , m ) of characteristic 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 .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41947/1/209-233-1-127_02330127.pd