$\wp$-adic continuous families of Drinfeld eigenforms of finite slope

par Shin Hattori (Tokyo City University)

mardi 10 mars 2020, 10:45 → 11:45 Europe/Paris

Bât. Braconnier, salle 112 (ICJ, Université Lyon 1)

Let $p$ be a rational prime and $q>1$ a $p$-power integer. Drinfeld modular forms are rigid analytic functions on the Drinfeld upper half plane over $\mathbb F_q((1/t))$ satisfying a similar transformation condition and holomorphy condition to elliptic modular forms. Though numerical computations suggest that they have interesting $\wp$-adic structures, we still have poor understanding of them.

In this talk, I will explain how to construct $\wp$-adic continuous families of Drinfeld eigenforms of finite slope using Teitelbaum's description of Drinfeld cuspforms via the Steinberg module, and also what we can say about slope zero Drinfeld cuspforms.