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Suppose we are given a Drinfeld Module $phi$ over $mathbb{F}_q(t)$ of rank $r$ and a prime ideal $mathfrak{l}$ of $mathbb{F}_q[T]$. In this paper, we prove that the reducibility of mod $mathfrak{l}$ Galois representation $${rm{Gal}}(mathbb{F}_q(T)^{rm{sep}}/mathbb{F}_q(T))rightarrow {rm{Aut}}(phi[mathfrak{l}])cong {rm{GL}}_r(mathbb{F}_mathfrak{l})$$ gives a bound on the degree of $mathfrak{l}$ which depends only on the rank $r$ of Drinfeld module $phi$ and the minimal degree of place $mathcal{P}$ where $phi$ has good reduction at $mathcal{P}$. Then, we apply this reducibility bound to study the Drinfeld module analogue of Serres uniformity problem.
Rank-2 Drinfeld modules are a function-field analogue of elliptic curves, and the purpose of this paper is to investigate similarities and differences between rank-2 Drinfeld modules and elliptic curves in terms of supersingularity. Specifically, we
In this paper, we study the surjectivity of adelic Galois representation associated to Drinfeld $mathbb{F}_q[T]$-modules over $mathbb{F}_q(T)$ of rank $2$ in the cases when $q$ is even or $q=3$.
We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular polynomials attached to Drinfeld modules.
We fix data $(K/F, E)$ consisting of a Galois extension $K/F$ of characteristic $p$ global fields with arbitrary abelian Galois group $G$ and a Drinfeld module $E$ defined over a certain Dedekind subring of $F$. For this data, we define a $G$-equivar
We give an effective algorithm to determine the endomorphism ring of a Drinfeld module, both over its field of definition and over a separable or algebraic closure thereof. Using previous results we deduce an effective description of the image of the