Completions of local rings with an isolated singularity
Let \(T\) be a complete local ring and let \(p\) be the characteristic of its residue field. The problem here is the existence of a local ring \(R\) with an isolated singularity, such that \(T\) is the completion of \(R\). The author shows that such a ring \(R\) exists if and only if for all non- maximal primes \(P \subset T\), the image of \(p\) in \(T_ P\) is either 0 or regular. This condition is easily shown to be necessary. The existence of \(R\), when the condition holds, is proved constructively starting with the prime subring \(R_ 0\) of \(T\) and extending carefully \(R_ 0\) to a ring \(R\) with \(\widehat R = T\).
scientific article; zbMATH DE number 554220
scientific article