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 and trace maps.
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