An explicit bound on reducibility of mod $\mathfrak{l}$ Galois image for Drinfeld modules of arbitrary rank and its application on the uniformity problem

Publication date: 28 August 2021

Abstract: Suppose we are given a Drinfeld Module

p h i

over

m a t h b b F_{q} (t)

of rank

r

and a prime ideal

m a t h f r a k l

of

m a t h b b F_{q} [T]

. In this paper, we prove that the reducibility of mod

m a t h f r a k l

Galois representation

{ m{Gal}}(mathbb{F}_q(T)^{ m{sep}}/mathbb{F}_q(T)) ightarrow { m{Aut}}(phi[mathfrak{l}])cong { m{GL}}_r(mathbb{F}_mathfrak{l})

gives a bound on the degree of

m a t h f r a k l

which depends only on the rank

r

of Drinfeld module

p h i

and the minimal degree of place

m a t h c a l P

where

p h i

has good reduction at

m a t h c a l P

. Then, we apply this reducibility bound to study the Drinfeld module analogue of Serre's uniformity problem.

This page was built for publication: An explicit bound on reducibility of mod $\mathfrak{l}$ Galois image for Drinfeld modules of arbitrary rank and its application on the uniformity problem

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6376227)