Let $X$ be a smooth affine variety over $\mathbb{C}$ and let $\mathcal{D}\_X$ be its algebra of differential operators.


Consider $\mathcal{C}=\mathcal{D}\_X$-$\text{mod}$, the stable $\infty$ category of $\mathcal{D}\_X$-modules (unbounded complexes of $\mathcal{D}\_X$-modules localized at quasi-isomorphisms). Assuming this is the correct category, i've seen in many places the statement that this category is compactly generated. I haven't been able to find a proof of this however. So...



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> Is $\mathcal{C}$ compactly generated? If so, who are the compact objects in $\mathcal{C}$? Where can I find a good reference for this?
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Who are the compact generators in the derived category of $\mathcal{D}_X$-modules?
One place where this is discussed is


*Drinfeld, Vladimir; Gaitsgory, Dennis*, [**On some finiteness questions for algebraic stacks**](http://dx.doi.org/10.1007/s00039-012-0204-5), Geom. Funct. Anal. 23, No. 1, 149-294 (2013). [ZBL1272.14005](https://zbmath.org/?q=an:1272.14005).


