Abstract :
It this note we prove the following theorem. Letπalg1(A1C) be the algebraic fundamental group of the affine line overC, whereCis the completion of the algebraic closure ofFq((1/T)), andFqis a field withqelements. IfFqhas at least four elements, then we show that there is a continuous surjectionπalg1(A1C)→imageSL2?(A/I)/{+ ±1}, whereA=Fq[T] and the inverse limit is over the family of non-zero, proper ideals ofA. This result is proved by using the moduli of DrinfelʹdA-modules of rank two overCwithI-level structures; these curves give (tamely) ramified covers of the line and the tame ramification is removed using a variant of Abhyankarʹs lemma.
