Local rings of bounded Cohen-Macaulay type
Commutative Algebra
2007-05-23 v2 Rings and Algebras
Abstract
Let (R,m,k) be a local Cohen-Macaulay (CM) ring of dimension one. It is known that R has finite CM type if and only if R is reduced and has bounded CM type. Here we study the one-dimensional rings of bounded but infinite CM type. We will classify these rings up to analytic isomorphism (under the additional hypothesis that the ring contains an infinite field). In the first section we deal with the complete case, and in the second we show that bounded CM type ascends to and descends from the completion. In the third section we study ascent and descent in higher dimensions and prove a Brauer-Thrall theorem for excellent rings.
Cite
@article{arxiv.math/0211411,
title = {Local rings of bounded Cohen-Macaulay type},
author = {Graham J. Leuschke and Roger Wiegand},
journal= {arXiv preprint arXiv:math/0211411},
year = {2007}
}
Comments
13 pages, revised and corrected