Nagata compactification for algebraic spaces

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.

49 pages, various clarifications and bugfixes

References in corpus (3)

• Noetherian approximation of algebraic spaces and stacks
• Existence and properties of geometric quotients
• Nagata's embedding theorem

Cited by in corpus (1)

• The basic geometry of Witt vectors, II: Spaces