Pr\"ufer algebraic spaces
Algebraic Geometry
2016-05-30 v3
Abstract
This is the first in a series of two papers concerned with relative birational geometry of algebraic spaces. In this paper, we study Pr\"ufer spaces and Pr\"ufer pairs of algebraic spaces that generalize spectra of Pr\"ufer rings. As a particular case of Pr\"ufer 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.
Cite
@article{arxiv.1101.3199,
title = {Pr\"ufer algebraic spaces},
author = {Michael Temkin and Ilya Tyomkin},
journal= {arXiv preprint arXiv:1101.3199},
year = {2016}
}
Comments
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