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GAGA is short for Serre's 1956 paper "Géometrie Algébrique et Géométrie Analytique". The tag refers not only to that paper, but also to the way of thinking introduced by it.
15
votes
Algebraic de Rham cohomology vs. analytic de Rham cohomology
If $X$ is smooth and proper, GAGA does in fact suffice (despite the observation that $d$ is not $\mathcal{O}_X$-linear: One obtains a comparison map of hypercohomology spectral sequences; it is an isomorphism … on the $E_2$ page by GAGA, and thus on the $E_\infty$ page. …