Abstract
We construct an explicit free resolution T for a maximal Cohen-Macaulay module M over a local complete intersection of codimension 2 with infinite residue field. The resolution is minimal when the module M is a sufficiently high syzygy. Our starting point is a layered free resolution L, described in [7], of length 2 over a regular local ring. We provide explicit formulas for the differential in T in terms of the differential and homotopies on the finite resolution L. One application of our construction is to describe Ulrich modules over a codimension 2 quadratic complete intersection.
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