Say f: X → Y is a morphism of schemes. The sheaf direct image functor f<sub>★</sub> always has a left adjoint, namely the sheaf inverse image functor f<sup>★</sup> (with tensoring). >Under what conditions do we know that f<sub>★</sub> has a *right* adjoint? What is it? **Edit:** What I'm looking for are appropriately general *sufficient* conditions... Certainly exactness of f<sub>★</sub> is a *necessary* condition. As well, perhaps I should be clear that I'm not assuming *quasi-coherence* in these categories of O<sub>X</sub>-Modules