On relative birational geometry and Nagata's compactification

Abstract

In 2011, the first author introduced (relative) Riemann-Zariski spaces corresponding to a morphism of schemes and established their basic properties. In this paper we clarify that theory and extend it to morphisms between algebraic spaces. As an application, a new proof of Nagata's compactification theorem for algebraic spaces is obtained.

28 pages, comments are welcome

References in corpus (4)

• Desingularization of quasi-excellent schemes in characteristic zero
• Noetherian approximation of algebraic spaces and stacks
• Étale dévissage, descent and pushouts of stacks
• Ferrand's pushouts for algebraic spaces

Cited by in corpus (1)

• Ferrand's pushouts for algebraic spaces