Let S be a scheme. Let Z ⊂ S be a closed subscheme. Let b : S′ —> S be the blowing up of Z in S. Let g : X —> Y be an affine morphism of schemes over S. Let F be a quasi-coherent sheaf on X. Let g′ : X ×S S′ —> Y ×S S′ be the base change of g. Let F′ be the strict transform of F relative to b. Then g′∗F′ is the strict transform of g∗F. See Tag 080G.
This tag has one of the densest initial trees in the project: