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arXiv · 1410.0185

A special chain theorem for the embedding dimension

S. Bouchiba·S. Kabbaj
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Abstract

This paper establishes an analogue of the special chain theorem for the embedding dimension of polynomial rings, with direct application on the (embedding) codimension. In particular, we recover a classic result on the transfer of regularity to polynomial rings (initially proved via a combination of Serre's result on finite global dimension and Hilbert theorem on syzygies). A second application characterizes regularity in general settings of localizations of polynomial rings, including Nagata rings and Serre's conjecture rings.

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S. Bouchiba, S. Kabbaj. 2017-01-20. A special chain theorem for the embedding dimension. https://arxiv.org/abs/1410.0185

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