## Well-generated category

Let $f:X\rightarrow S$ be a proper morphism of finite-dimensional complex spaces and assume that the fibers are n-dimensional. By means of the Brown-Neeman representability theorem, I want to construct formally the right adjoint of the right exact functor $R^{n}f_{*}$. We know that the category $D(QC/X)$ is not compactly generated.

Question: Is this category well-generated in the sense of Neeman (see Henning Krause "On Neeman's well generated triangulated categories" google) ?

Remark: Of course, Ramis-Ruget-Verdier relative duality gives directly that $H^{-n}(f^{!}-)$ is the right adjoint.

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