Alladi Ramakrishnan Hall

Families of Drinfeld modular forms for GL(N)

Marc-Hubert Nicole

Institut de Mathematiques de Luminy

The theory of families of classical modular forms was developed by Hida,
Coleman, Mazur et al., and includes p-adic modular forms e.g. overconvergent
modular forms.

In this talk, we shall explain the key components of an analogous theory in
the realm of function fields that is, for so-called Drinfeld modular forms.

In particular, there exists for GL(n) a theory of Hida families of ordinary
modular forms, as well as a continuous analogue of the theory of Coleman
families in finite slope. Further, a classicality theorem states that an
overconvergent Drinfeld modular form with sufficient « small » slope is
automatically classical.

Joint work with G. Rosso (Montréal)