A going-down theorem for real spectra
The aim of this note is to obtain the following theorem: Let \(\psi\) : \(A\to B\) be a regular homomorphism of noetherian rings, A excellent, and \(\psi^*:\quad Y\to X\) the corresponding map of real spectra. For any prime cones \(\alpha '\to \alpha\) in X and \(\beta\in Y\) with \(\psi^*\beta =\alpha\), there is \(\beta '\in Y\) with \(\beta '\to \beta,\) \(\psi^*\beta '=\alpha ',\) \(ht(\beta ')=ht(\alpha ').\) For the notion of the real spectrum the author refers to \textit{M. Coste} and \textit{M.-F. Roy}, Contemp. Math. 8, 27-59 (1982; Zbl 0485.14007).
scientific article; zbMATH DE number 4127380