English

Relative-Hyper GAGA Theorem

Algebraic Geometry 2024-09-11 v3

Abstract

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.

Keywords

Cite

@article{arxiv.2409.01481,
  title  = {Relative-Hyper GAGA Theorem},
  author = {Eita Haibara and Taewan Kim},
  journal= {arXiv preprint arXiv:2409.01481},
  year   = {2024}
}

Comments

12 pages. We updated proposition 3.1.1, lemma 3.1.4. Comments are welcome !

R2 v1 2026-06-28T18:31:59.406Z