#### 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)

Done