PERFECTOID DRINFELD MODULAR FORMS

Marc-Hubert Nicole (1, 2) , Giovanni Rosso (3)

1 I2M - Institut de Mathématiques de Marseille
2 IRL CRM-CNRS - International Research Lab
3 Concordia University [Montreal]

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 GLpnq.

Mots clés: p-adic families; Drinfeld modular forms; perfectoid spaces.

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Marc-Hubert Nicole, Giovanni Rosso. PERFECTOID DRINFELD MODULAR FORMS. Journal de Théorie des Nombres de Bordeaux, In press, Iwasawa 2019. ⟨hal-02528893v2⟩