Are complete intersections complete intersections?
Commutative Algebra
2011-09-23 v1
Abstract
A commutative local ring is generally defined to be a complete intersection if its completion is isomorphic to the quotient of a regular local ring by an ideal generated by a regular sequence. It has not previously been determined whether or not such a ring is necessarily itself the quotient of a regular ring by an ideal generated by a regular sequence. In this article, it is shown that if a complete intersection is a one dimensional integral domain, then it is such a quotient. However, an example is produced of a three dimensional complete intersection domain which is not a homomorphic image of a regular local ring, and so the property does not hold in general.
Cite
@article{arxiv.1109.4921,
title = {Are complete intersections complete intersections?},
author = {Raymond C. Heitmann and David A. Jorgensen},
journal= {arXiv preprint arXiv:1109.4921},
year = {2011}
}