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arXiv · 1404.2641

Formal Fibers of Prime Ideals in Polynomial Rings

William Heinzer·Christel Rotthaus·Sylvia Wiegand
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Abstract

Let (R,m) be a Noetherian local domain of dimension n that is essentially finitely generated over a field and let R^ denote the m-adic completion of R. Matsumura has shown that n-1 is the maximal height possible for prime ideals of R^ in the generic formal fiber of R. In this article we prove that every prime ideal of R^ that is maximal in the generic formal fiber of R has height n-1. We also present a related result concerning the generic formal fibers of certain extensions of mixed polynomial-power series rings.

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William Heinzer, Christel Rotthaus, Sylvia Wiegand. 2014-04-09. Formal Fibers of Prime Ideals in Polynomial Rings. https://arxiv.org/abs/1404.2641

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