Perfectoid Drinfeld Modular Forms
Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 3.2, pp. 1045-1067.

In the first part, we revisit Drinfeld modular curves associated to GL(2) from the perfectoid point of view, and we show how to recover (a perfectized) part of the theory of overconvergent π-adic Drinfeld modular forms. In the second part, we review open problems for families of Drinfeld modular forms for GL(n).

Dans la première partie, nous revenons sur les courbes modulaires de Drinfeld associée à GL(2) en adoptant le point de vue perfectoïde, et nous montrons comment récupérer une portion (perfectisée) de la théorie des formes modulaires de Drinfeld π-adiques surconvergentes. Dans la seconde partie, nous présentons quelques problèmes ouverts portant sur les familles de formes modulaires de Drinfeld pour GL(n).

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DOI: 10.5802/jtnb.1187
Classification: 11F33, 11F52, 11G09
Keywords: $p$-adic families, Drinfeld modular forms, perfectoid spaces
Nicole, Marc-Hubert 1; Rosso, Giovanni 2

1 Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Université de Caen Basse Normandie 14032 Caen Cedex, France
2 Department of Mathematics and Statistics Montréal, Québec, Canada
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Nicole, Marc-Hubert; Rosso, Giovanni. Perfectoid Drinfeld Modular Forms. Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 3.2, pp. 1045-1067. doi : 10.5802/jtnb.1187. http://www.numdam.org/articles/10.5802/jtnb.1187/

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