Given a smooth quasi-projective variety over $\mathbb{C}$ and bounded complexes of vector bundles $(P,d)$ and $(P',d')$ with compactly supported cohomology. It is well-known that such complexes satisfy Serre-duality.

Question: Is there a reference which proves Serre duality using compactly supported Dolbeault cohomology?

The proof I have in mind is the standard proof of Serre duality for projective varieties, but there are two potential points of difficulty.

a) I remember in Serre's original paper there are some tricky points of topology on Frechet spaces which are complicated. I haven't actually seen the compactly supported Dolbeault theory used in any other papers since then.

b) GAGA for sheaves with compactly supported cohomology.