Relative-Hyper GAGA Theorem

In this paper, we provide a relative hypercohomology version of Serre’s GAGA theorem. We prove that the relative hypercohomology of a complex of sheaves on a complex projective variety is isomorphic to the relative hypercohomology of its analytification, with respect to an open or closed subvariety. This result implies Serre’s original GAGA theorem.