Cônes locaux et complétions

Abstract

Let A be a local ring; let  denote the completion of A and Spec r A,Spec R  the real spectra of A and Â,respectively. The author studies the fibers of the canonical morphism Spec r  → Spec r A, for an excellent ring A, and computes its images. Two applications are given: an existence theorem for real valuations in excellent rings, and an Artin-Lang homomorphism theorem for global analytic functions