Abstract
We introduce a weak order ideal property that suffices for establishing the Evans–Griffith Syzygy Theorem. We study this weak order ideal property in settings that allow for comparison between homological algebra over a local ring R versus a hypersurface ring R ̄ = R / ( x n ) . Consequently we solve some relevant cases of the Evans–Griffith syzygy conjecture over local rings of unramified mixed characteristic p , with the case of syzygies of prime ideals of Cohen–Macaulay local rings of unramified mixed characteristic being noted. We reduce the remaining considerations to modules annihilated by p s , s > 0 , that have finite projective dimension over a hypersurface ring.
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