Prüfer algebraic spaces

Abstract

This is the first in a series of two papers concerned with relative birational geometry of algebraic spaces. In this paper, we study Prüfer spaces and Prüfer pairs of algebraic spaces that generalize spectra of Prüfer rings. As a particular case of Prüfer spaces we introduce valuation algebraic spaces, and use them to establish valuative criterion of universal closedness that sharpens the standard criterion. In the sequel paper, we will introduce a version of Riemann-Zariski spaces, and will prove Nagata compactification theorem for algebraic spaces.

This is a major revision of the first version. In particular, the section about Ferand's pushouts has been extended and split off into a separate paper: arXiv:1305.6014