Let $X$ be a scheme and let $D_{qoch}(X)$ and $D^b_{coh}(X)$ be the unbounded derived category of quasi-coherent sheaves and bounded derived category of coherent sheaves on $X$, respectively.

$D^b_{coh}(X)$ is closely related to the geometry of $X$ and has been intensively studied, see for example Huybrechts's book. On the other hand, $D_{qcoh}(X)$ has also been studied but its categorical structure is more complicated. For example, the injective resolutions in $D_{qcoh}(X)$ are actually h-injective complexes and more difficult to construct than the injective resolutions $D^b_{coh}(X)$.

My question is: is there any place that $D_{qcoh}(X)$ rather than $D^b_{coh}(X)$ plays an essential role? By "essential" I mean that $D_{qcoh}(X)$ is more than just an auxiliary tool.