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Nagata compactification for algebraic spaces

Published online by Cambridge University Press:  13 July 2012

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)

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.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2012

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