Say f: X &rarr; Y is a morphism of schemes.  The sheaf direct image functor f<sub>&#9733;</sub> always has a left adjoint, namely the sheaf inverse image functor f<sup>&#9733;</sup> (with tensoring).

>Under what conditions do we know that f<sub>&#9733;</sub> has a *right* adjoint?  What is it?

**Edit:** What I'm looking for are appropriately general *sufficient* conditions...  Certainly exactness of f<sub>&#9733;</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