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 2 and trace maps.
Highlights
Abstract. — We construct an integral model of the perfectoid modular curve
Theorem 0.1. — The inverse limit X(N p∞) = ←lim−n X(N pn) is a perfectoid formal scheme over Spf Zcpyc whose analytic generic fiber is naturally isomorphic to the perfectoid modular curve X(N p∞)
We prove the cohomological vanishing of Theorem 0.2 and its comparison with the cohomology of the perfectoid modular curve
Summary
An integral model of the perfectoid modular curve Tome 8 (2021), p. LICENCE INTERNATIONALE D’ATTRIBUTION CREATIVE COMMONS BY 4.0. Https://creativecommons.org/licenses/by/4.0/ L’accès aux articles de la revue « Journal de l’École polytechnique — Mathématiques » (http://jep.centre-mersenne.org/), implique l’accord avec les conditions générales d’utilisation (http://jep.centre-mersenne.org/legal/)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
