Analytic Deviation One Ideals and Test Modules

Let A be a Cohen-Macaulay local ring of dimension d and I an ideal in A. Let M be a finitely generated maximal Cohen-Macaulay A-module. Let I be a locally complete intersection ideal of analytic deviation one and reduction number at most one. We prove that the polynomial given by $length(Tor^{A}_{1}(M,A/I^{n+1}))$ either has degree d-1 or $F_I(M)$ is a free$F(I)-$$module.

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