Familles de formes modulaires de Drinfeld pour le groupe g\'en\'eral lin\'eaire
Marc-Hubert Nicole, Giovanni Rosso

TL;DR
This paper develops a Hida theory for Drinfeld modular forms over function fields, constructs families of forms varying with weight, and proves a classicity result for small slope overconvergent forms.
Contribution
It introduces a Hida theory framework for rank r Drinfeld modular forms, constructs continuous families in the finite slope case, and establishes a classicity criterion for small slope forms.
Findings
Established Hida theory for Drinfeld modular forms of rank r.
Constructed families of forms varying with weight.
Proved classicity for small slope overconvergent forms.
Abstract
Let be a function field over , its ring of regular functions outside a place and a prime ideal of . First, we develop Hida theory for Drinfeld modular forms of rank which are of slope zero for a suitably defined Hecke operator . Second, we show the existence in the finite slope case of families of Drinfeld modular forms varying continuously with respect to the weight. Finally, we show a classicity result: an overconvergent Drinfeld modular form of sufficiently small slope with respect to the weight is a classical Drinfeld modular form.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
