Lecture Room B, 4th Floor, The 3rd General Building , NTHU + Cisco WebEx, Physical+Online Seminar
(實體+線上演講 清大綜合三館Lecture Room B+ Cisco WebEx)
Triviality of the Hecke Action on Ordinary Drinfeld Cuspforms of Level $\Gamma_1(t^n)$
Shin Hattori (Tokyo City University)
Abstract
Let
be a rational prime,
a
-power integer and
a non-constant irreducible polynomial in
. The notion of Drinfeld modular form is an analogue over
of that of elliptic modular form. The expectation is that there should be a deep
-adic theory of Drinfeld modular forms which is comparable to the elliptic analogue.
However,
-adic properties of Drinfeld modular forms are less well understood than the
-adic elliptic case, and sometimes classical methods do not work or yield nothing useful (e.g. no eigenvariety so far).
In this talk, as an example of such unusual phenomena, I will explain that all Hecke operators act trivially on the space of ordinary Drinfeld cuspforms of level
for any positive integer
. It suggests that
-adic Hida families of tame level one should be trivial. It also gives a counterexample to Gekeler's question, which asks if the weak multiplicity one holds for Drinfeld modular forms when the weight is fixed.
Meeting number (access code): 2516 495 4195
Meeting password: zBJTe6PFX57