I don't know the meaning of geometrically injective morphism f of schemes.
What's the definition of "geometrically injective"?
I can't find it. I hope your answer.
Thanks.
I don't know the meaning of geometrically injective morphism f of schemes. What's the definition of "geometrically injective"? I can't find it. I hope your answer. Thanks. 


A map of schemes $f \colon X \to Y$ is geometrically injective if it is injective on geometric points, i.e. points with values in an algebraic closed field. In more detail, let $K$ be an algebraically closed field. For all pairs of maps ($K$valued points) $x, y \colon \operatorname{Spec}(K) \to X$ such that they have the same image on $Y$, i.e $f \circ x = f \circ y$ then $x = y$. In other words the map $$ \operatorname{Hom}(\operatorname{Spec}(K), X) \longrightarrow \operatorname{Hom}(\operatorname{Spec}(K), Y) $$ given by composition with $f$, is injective for every algebraically closed field $K$. 


I don't find link to add comment. You can find the various equivalent condition for radicial morphism and its proof in "Altman & Kleiman, Introduction to Grothendieck Duality Theory" on page 119. 

