Torsion of Drinfeld modules and equicharacteristic unimodular Galois covers
Abstract
We prove that the groups PSL(r,qd) can be realized Fq(T)-regularly as Galois groups over the purely transcendental field Fq(T)(t1,...,tr-1) if r is even and r/2 is coprime to qd-1. The method is to use twisted moduli schemes of Drinfeld modules (a la Shih). If one has sufficient control over modular forms, it can be made into an algorithm to find explicit equations. We do this for PSL(2,q2) using Drinfeld modular forms.
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