[Un modèle entier de la courbe modulaire perfectoïde]
Nous construisons un modèle entier de la courbe modulaire perfectoïde. Avec cet objet nous montrons des résultats d’annulation de la cohomologie cohérente au niveau perfectoïde. Nous utilisons un théorème de dualité locale au niveau fini pour obtenir une dualité pour la cohomologie cohérente au niveau infini. Finalement, en considérant le faisceau structural, nous obtenons une description du dual de la cohomologie complétée en termes des formes modulaires cuspidales de poids et des traces normalisées.
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.
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Keywords: Perfectoid modular curve, completed cohomology, coherent cohomology
Mot clés : Courbe modulaire perfectoïde, cohomologie complétée, cohomologie cohérente
Juan Esteban Rodríguez Camargo 1
CC-BY 4.0
@article{JEP_2021__8__1193_0,
author = {Juan Esteban Rodr{\'\i}guez Camargo},
title = {An integral model of the perfectoid modular curve},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {1193--1224},
publisher = {\'Ecole polytechnique},
volume = {8},
year = {2021},
doi = {10.5802/jep.170},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.170/}
}
TY - JOUR AU - Juan Esteban Rodríguez Camargo TI - An integral model of the perfectoid modular curve JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 1193 EP - 1224 VL - 8 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.170/ DO - 10.5802/jep.170 LA - en ID - JEP_2021__8__1193_0 ER -
%0 Journal Article %A Juan Esteban Rodríguez Camargo %T An integral model of the perfectoid modular curve %J Journal de l’École polytechnique — Mathématiques %D 2021 %P 1193-1224 %V 8 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.170/ %R 10.5802/jep.170 %G en %F JEP_2021__8__1193_0
Juan Esteban Rodríguez Camargo. An integral model of the perfectoid modular curve. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 1193-1224. doi : 10.5802/jep.170. https://jep.centre-mersenne.org/articles/10.5802/jep.170/
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