Are complete intersections complete intersections?

Details Are complete intersections complete intersections? Are complete intersections complete intersections?

2011-09-22

arxiv.org/abs/1109.4921v1

Mathematics

Commutative Algebra

Scientific paper

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.

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