### abstract

- In [3], Ferrand studied schematic pushouts of the form Open image in new window , where \(f:T\rightarrow Y\) is an affine morphism and \(g:T\hookrightarrow Z\) is a closed immersion. When f is finite such pushout is called pinching or pinching of Z with respect to f. Although studying pinchings was, probably, Ferrand's main motivation, he realized that the “right generality”, which allows one to prove all the fundamental results, is obtained by weakening the finiteness assumption on f. In the current paper we study the case of algebraic spaces Y, Z, and T with the same assumptions on f and g. We call such a triple \({\mathscr {P}}=(T;Y,Z)\) a Ferrand pushout datum. If \({\mathscr {P}}\) admits a pushout X in the category of algebraic spaces such that the morphisms \(Y\rightarrow X\) and \(Z … Let \(g:T\hookrightarrow Z\) be a closed immersion. If \(f:T\rightarrow Y\) is also a closed immersion, then the pinching Open image in new window can be viewed as the …