Geodesic
Overconvergent Modular Forms and Perfectoid Shimura Curves
Documenta mathematica, Tome 22 (2017), pp. 191-262.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We give a new construction of overconvergent modular forms of arbitrary weights, defining them in terms of functions on certain affinoid subsets of Scholze's infinite-level modular curve. These affinoid subsets, and a certain canonical coordinate on them, play a role in our construction which is strongly analogous with the role of the upper half-plane and its coordinate `$z$' in the classical analytic theory of modular forms. As one application of these ideas, we define and study an overconvergent Eichler-Shimura map in the context of compact Shimura curves over $\Bbb{Q}$, proving stronger analogues of results of Andreatta-Iovita-Stevens.
Classification : 11F33, 11F70, 11G18
Keywords: affinoid subsets, overconvergent Eichler-Shimura map 
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     author = {Chojecki, Przemys{\l}aw and Hansen, D. and Johansson, C.},
     title = {Overconvergent {Modular} {Forms} and {Perfectoid} {Shimura} {Curves}},
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Chojecki, Przemysław; Hansen, D.; Johansson, C. Overconvergent Modular Forms and Perfectoid Shimura Curves. Documenta mathematica, Tome 22 (2017), pp. 191-262. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a45/