Finding Endomorphisms of Drinfeld modules

TL;DR

This paper presents algorithms to compute the endomorphism ring of Drinfeld modules and to determine isogeny relations, providing effective tools for understanding their algebraic and Galois-theoretic properties.

Contribution

It introduces effective algorithms for computing endomorphism rings and isogenies of Drinfeld modules, extending previous theoretical results to practical computational methods.

Findings

Algorithm for endomorphism ring determination

Effective criteria for isogeny detection

Description of Galois representation images

Abstract

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.