Geodesic
Overconvergent Modular Forms and Perfectoid Shimura Curves
Documenta mathematica, Tome 22 (2017), pp. 191-262
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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 Q, proving stronger analogues of results of Andreatta-Iovita-Stevens.
DOI : 10.4171/dm/564
Classification : 11F33, 11F70, 11G18
Mots-clés : affinoid subsets, overconvergent Eichler-Shimura map 
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     author = {D. Hansen and Przemys{\l}aw Chojecki and C. Johansson},
     title = {Overconvergent {Modular} {Forms} and {Perfectoid} {Shimura} {Curves}},
     journal = {Documenta mathematica},
     pages = {191--262},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/564},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/564/}
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D. Hansen; Przemysław Chojecki; C. Johansson. Overconvergent Modular Forms and Perfectoid Shimura Curves. Documenta mathematica, Tome 22 (2017), pp. 191-262. doi: 10.4171/dm/564

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