Ferrand's pushouts for algebraic spaces

Abstract

We extend Ferrand's results about pushouts of schemes to the category of algebraic spaces. We call the corresponding class of pushouts Ferrand's pushouts. They will be used in our sequel works to extend the notions of valuation rings and Riemann-Zariski spaces to the category of algebraic spaces, and to obtain a new proof of Nagata's compactification theorem for algebraic spaces.