Prüfer algebraic spaces

Michael Temkin, Ilya Tyomkin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 languageEnglish
Pages (from-to)1283-1318
Number of pages36
JournalMathematische Zeitschrift
Issue number3-4
StatePublished - 1 Apr 2017


  • Algebraic spaces
  • Prüfer pairs

ASJC Scopus subject areas

  • Mathematics (all)


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