On the completion of excellent rings in characteristic p\(>0\) (Q1073109)

The paper deals with the following Grothendieck problem: If A is an excellent ring and \({\mathfrak m}\) an ideal of A, is the \({\mathfrak m}\)-adic completion of A an excellent ring ? The present author considers a case when A is an algebra of finite type over a local excellent ring C of characteristic p\(>0\) and dimension 1. It is shown that there is a positive answer for C complete or for C containing a field k of characteristic p\(>0\) and finite over \(k[C^ p]\).