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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 adelic Galois representation associated to the Drinfeld module, up to commensurability. We also give an effective algorithm to decide whether two Drinfeld modules are isogenous, again both over their field of definition and over a separable or algebraic closure thereof.
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.
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 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
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
We study the dynamics of the map endomorphism of N-dimensional projective space defined by f(X)=AX^d, where A is a matrix and d is at least 2. When d>N^2+N+1, we show that the critical height of such a morphism is comparable to its height in moduli s