a1 Department of Mathematics, Stanford University, Building 380, Stanford, CA 94305, USA (email@example.com)
a2 Department of Mathematics, University of Washington, Seattle, WA 98195, USA (firstname.lastname@example.org)
a3 Department of Mathematics, University of California, Berkeley, 970 Evans Hall, Berkeley, CA 94720, USA (email@example.com)
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.
(Received November 17 2009)
(Accepted November 12 2010)
AMS 2010 Mathematics subject classification
To the memory of Masayoshi Nagata