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arXiv · 2304.02900

Ext modules related to syzygies of the residue field

Yuya Otake
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Abstract

Let R be a commutative noetherian ring. In this paper, we find out close relationships between the module M being embedded in a module of projective dimension at most n and the (n+1)-torsionfreeness of the nth syzygy of M. As an application, when R is local with residue field k, we compute the dimensions as k-vector spaces of Ext modules related to syzygies of k.

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Yuya Otake. 2023-04-06. Ext modules related to syzygies of the residue field. https://arxiv.org/abs/2304.02900

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