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 criteria of separatedness and properness that sharpen the standard criteria. In a sequel paper, we introduce a version of Riemann–Zariski spaces, and prove Nagata’s compactification theorem for algebraic spaces.
Original language | American English |
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Pages (from-to) | 1283-1318 |
Number of pages | 36 |
Journal | Mathematische Zeitschrift |
Volume | 285 |
Issue number | 3-4 |
DOIs | |
State | Published - 1 Apr 2017 |
Bibliographical note
Funding Information:Michael Temkin and Ilya Tyomkin were supported by the Israel Science Foundation (Grant No. 1018/11).
Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
Keywords
- Algebraic spaces
- Prüfer pairs