Prüfer algebraic spaces

Michael Temkin; Ilya Tyomkin

doi:10.1007/s00209-016-1748-0

Prüfer algebraic spaces

Michael Temkin, Ilya Tyomkin^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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
Pages (from-to)	1283-1318
Number of pages	36
Journal	Mathematische Zeitschrift
Volume	285
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-016-1748-0
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

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10.1007/s00209-016-1748-0

Cite this

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title = "Pr{\"u}fer 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 Pr{\"u}fer spaces and Pr{\"u}fer pairs of algebraic spaces that generalize spectra of Pr{\"u}fer rings. As a particular case of Pr{\"u}fer 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{\textquoteright}s compactification theorem for algebraic spaces.",

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note = "Funding Information: Michael Temkin and Ilya Tyomkin were supported by the Israel Science Foundation (Grant No. 1018/11). Publisher Copyright: {\textcopyright} 2016, Springer-Verlag Berlin Heidelberg.",

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AB - 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.

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Prüfer algebraic spaces

Abstract

Bibliographical note

Keywords

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