Completely Controlling the Dimensions of Formal Fiber Rings at Prime Ideals of Small Height

2016/04/14 by Fleming, Sarah M., Ji, Lena, Loepp, S. +3 · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.04176

Abstract

Let T be a complete equicharacteristic local (Noetherian) UFD of dimension 3 or greater. Assuming that |T| = |T/m|, where m is the maximal ideal of T, we construct a local UFD A whose completion is T and whose formal fibers at height one prime ideals have prescribed dimension between zero and the dimension of the generic formal fiber. If, in addition, T is regular and has characteristic zero, we can construct A to be excellent.

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