In the paper,
http://www.numdam.org/article/PMIHES_1966__29__95_0.pdf
Grothendieck proves the isomorphism between algebraic de Rham cohomology and Betti cohomology, i.e. for a smooth quasi-projective variety $X$ over $\mathbb{C}$, we have \begin{equation} H^i_{\text{dR}}(X/\mathbb{C}) \simeq H^i(X^{\text{an}},\mathbb{C}) \end{equation} The algebraic de Rham cohomology $H^i_{\text{dR}}(X/\mathbb{C})$ is the hypercohomology of the complex $\Omega^*_{X}$ of algebraic forms, while $H^i(X^{\text{an}},\mathbb{C})$ could also be computed as the hypercohomology of the holomorphic forms $\Omega^{h,*}_{X^{an}}$. Naively, it seems straightforward that a direct application of Serre's GAGA to the two complexes of forms would imply this isomorphism, but I remember someone mentions that this naive argument does not work, but why? References are sincerely appreciated!