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Creators/Authors contains: "David Eisenbud and Frank-Olaf Schreyer"

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  1. (, Contemporary mathematics)
    Let M be a finitely generated Cohen-Macaulay module of codimension m over a Gorenstein Ring R=S/I, where S is a regular ring. We show how to form a quasi-isomorphism ϕ from an R-free resolution of M to the dual of an R-free resolution of M∨:=ExtmR(M,R) using the S-free resolutions of R and M. The mapping cone of ϕ is then a Tate resolution of M, allowing us to compute the maximal Cohen-Macaulay approximation of M. "In the case when R is 0-dimensional local, and M is the residue field, the formula for ϕ becomes a formula for the socle of R generalizing a well-known formula for the socle of a zero-dimensional complete intersection. "When I⊂J⊂S are ideals generated by regular sequences, the R-module M=S/J is called a quasi-complete intersection, and ϕ was studied in detail by Kustin and Şega. We relate their construction to the sequence of `EagonNorthcott'-like complexes originally introduced by Buchsbaum and Eisenbud. 
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