Exercise 14, § 7

Let A be a local ring of Grothendieck. Now prove that the set of prime ideals p of A such that the ring A_p is regular is open in Spec(A) (let $\widehat{A}$ be the completion of A; one will use the exercise 5, Exercise 16 of VIII, § 5, and the fact that the canonical mapping Spec($\widehat{A}$) → Spec(A) is open). \*