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Nagata compactification for algebraic spaces

Part of: Algebraic geometry: Foundations Birational geometry

Published online by Cambridge University Press:  13 July 2012

Brian Conrad ,
Max Lieblich  and
Martin Olsson
Brian Conrad
Affiliation:
Department of Mathematics, Stanford University, Building 380, Stanford, CA 94305, USA (conrad@math.stanford.edu)
Max Lieblich
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA 98195, USA (lieblich@math.washington.edu)
Martin Olsson
Affiliation:
Department of Mathematics, University of California, Berkeley, 970 Evans Hall, Berkeley, CA 94720, USA (molsson@math.berkeley.edu)
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Abstract

We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian approximation for such algebraic spaces, generalizing earlier results in the case of schemes.

Keywords

algebraic spacesNagata compactificationNoetherian approximation

MSC classification

Secondary: 14A15: Schemes and morphisms 14E99: None of the above, but in this section
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 4 , October 2012 , pp. 747 - 814
Copyright
Copyright © Cambridge University Press 2012

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