More AG-related, but suppose I have a closed immersion of schemes $f:Y \to X.$ Suppose further that I have a map $g:Y \to Spec A$ for some A. When will the pushout of f and g exist in the category of schemes?
returning to K.S. Brown, the automatically-generated bibtex (coming from mathscinet) prints in all-caps: TITLE = {A{BSTRACT} {HOMOTOPY} {THEORY} {AND} {GENERALIZED} {SHEAF} {COHOMOLOGY}}
is it reasonable to de-cappify this, or will that screw up all the automated citation-counter robots or whatever?
@Dedalus, sufficient conditions are that $g$ is a closed immersion, or if $f$ has the further property that it is an isomorphism on reduced subschemes. Neither of these conditions use that the target of $g$ is affine.
