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arXiv · 1109.4921

Are complete intersections complete intersections?

Raymond C. Heitmann·David A. Jorgensen
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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.

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Raymond C. Heitmann, David A. Jorgensen. 2011-09-22. Are complete intersections complete intersections?. https://arxiv.org/abs/1109.4921

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