English

An integral model of the perfectoid modular curve

Number Theory 2021-06-24 v3

Abstract

We construct an integral model of the perfectoid modular curve. Studying this object, we prove some vanishing results for the coherent cohomology at perfectoid level. We use a local duality theorem at finite level to compute duals for the coherent cohomology of the integral perfectoid curve. Specializing to the structural sheaf, we can describe the dual of the completed cohomology as the inverse limit of the integral cusp forms of weight 22 and trace maps.

Keywords

Cite

@article{arxiv.2010.03463,
  title  = {An integral model of the perfectoid modular curve},
  author = {Juan Esteban Rodríguez Camargo},
  journal= {arXiv preprint arXiv:2010.03463},
  year   = {2021}
}

Comments

31 pages

R2 v1 2026-06-23T19:08:08.509Z