In , the first author introduced (relative) Riemann-Zariski spaces corresponding to a morphism of schemes and established their basic properties. In this article, 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.
Bibliographical noteFunding Information:
M.T. and I.T. were supported by the Israel Science Foundation (grant No. 1018/11). I.T. was also partially supported by the European FP7 IRG grant 248826.
© The Author(s) 2017.