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arXiv · 1407.0096

On Modules of Finite Projective Dimension

Sankar P. Dutta
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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 R of mixed characteristic p > 0, where p is a non-zero-divisor, if I is an ideal of finite projective dimension over R and p is in I or p is a non-zero-divisor on R/I, then every minimal generator of I is a non-zero-divisor. Hence if P is a prime ideal of finite projective dimension in a local ring R, then every minimal generator of P is a non-zero-divisor in R.

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Sankar P. Dutta. 2014-07-01. On Modules of Finite Projective Dimension. https://arxiv.org/abs/1407.0096

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