Torsion of Drinfeld modules and equicharacteristic unimodular Galois covers

Details Torsion of Drinfeld modules and equicharacteristic unimodular Galois covers Torsion of Drinfeld modules and equicharacteristic unimodular Galois covers

2002-09-03

arxiv.org/abs/math/0209023v1

Mathematics

Number Theory

14 pages, uses a4 style

Scientific paper

We prove that the groups PSL(r,q^d) can be realized F_q(T)-regularly as Galois groups over the purely transcendental field F_q(T)(t_1,...,t_{r-1}) if r is even and r/2 is coprime to q^d-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,q^2) using Drinfeld modular forms.

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