Nagata compactification for algebraic spaces
By Brian Conrad, Max Lieblich, Martin Olsson. Journal of the Institute of Mathematics of Jussieu, 2009
65 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a3e9d630299c8e5d8803b3e43df2cb863d4fff0d
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In Geometry and Topology
- D. Huybrechts
- James M. Borger
- Fumiharu Kato
- K. Fujiwara
- E. Markman
- Kieran G. O’Grady
- P. Stellari
- Emanuele Macrì
In Mathematical Physics
- D. Huybrechts
- James M. Borger
- Fumiharu Kato
- K. Fujiwara
- P. Stellari
- Emanuele Macrì
- E. Markman
- L. Hesselholt
Citations in the corpus
- Lectures on K3 Surfaces (2016, methodology): “This is provided by the Nagata compactification theorem, see [127].”
- Foundations of Rigid Geometry I (2013, background): “Finally, we include here the statement of the compactification theorem for algebraic spaces ([34], [26]):”
- The basic geometry of Witt vectors. II: Spaces (2010, background): “(See Conrad–Lieblich–Olsson [ 13 ], A.1.2.) And conversely, any algebraic space in the sense of Raynaud–Gruson is the quotient of a disjoint union of affine schemes by an etale equivalence relation which is a scheme, necessarily separated; therefore it is”