Abstract
We address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the embeddability problem and prove important reductions and special cases of the order ideal conjecture. In particular, we derive that, in any local ring of mixed characteristic , where is a nonzero divisor, if is an ideal of finite projective dimension over and or is a nonzero divisor on , then every minimal generator of is a nonzero divisor. Hence, if is a prime ideal of finite projective dimension in a local ring , then every minimal generator of is a nonzero divisor in .
Citation
S. P. Dutta. "On modules of finite projective dimension." Nagoya Math. J. 219 87 - 111, September 2015. https://doi.org/10.1215/00277630-3140702
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