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- Title
Prüfer algebraic spaces.
- Authors
Temkin, Michael; Tyomkin, Ilya
- 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.
- Publication
Mathematische Zeitschrift, 2017, Vol 285, Issue 3/4, p1283
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-016-1748-0