Syzygy Theorems via Comparison of Order Ideals on a Hypersurface

2011/06/18 by Phillip A. Griffith, Griffith, Phillip A., Alexandra Seceleanu +1
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC

paper · pdf · doi:10.48550/arxiv.1106.3663

To appear in JPAA

arxiv created 2011/06/18 · arxiv updated 2011/06/21

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/(xⁿ). 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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