Determinantal ideals without minimal free resolutions

Abstract

Let R be a Noetherian commutative ring with, unit element, and X ij be variables with 1 ≤ i ≤ m and 1 ≤ j ≤ n . Let S = R[x ij ] be the polynomial ring over R , and I t be the ideal in S , generated by the t × t minors of the generic matrix (x ij ) ∈ M m, n (S) . For many years there has been considerable interest in finding a minimal free resolution of S/I t , over arbitrary base ring R . If we have a minimal free resolution P. over R = Z, the ring of integers, then R′ ⊗ z P . is a resolution of S/I t over the base ring R′ .