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The Stacks project

Lemma 33.36.5. Let p > 0 be a prime number. Let S be a scheme in characteristic p. Let f : X \to Y be a morphism of schemes over S . Then the diagram

\xymatrix{ X \ar[d]_ f \ar[r]_{F_{X/S}} & X^{(p)} \ar[d]^{f^{(p)}} \\ Y \ar[r]^{F_{Y/S}} & Y^{(p)} }

commutes.

Proof. This follows from Lemma 33.36.2 and the definitions. \square

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