### Abstract

It this note we prove the following theorem. Let Π^{alg}_{1}(A^{1}_{C}) be the algebraic fundamental group of the affine line over C, where C is the completion of the algebraic closure of F_{q}((1/T)), and F_{q} is a field with q elements. If F_{q} has at least four elements, then we show that there is a continuous surjection Π^{alg}_{1}(A^{1}_{C}) → _{←}lim SL_{2}(A/I)/{+ ± 1}, where A = F_{q}[T] and the inverse limit is over the family of non-zero, proper ideals of A. This result is proved by using the moduli of Drinfel'd A-modules of rank two over C with I-level structures; these curves give (tamely) ramified covers of the line and the tame ramification is removed using a variant of Abhyankar's lemma.

Original language | English (US) |
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Pages (from-to) | 414-418 |

Number of pages | 5 |

Journal | Journal of Number Theory |

Volume | 59 |

Issue number | 2 |

DOIs | |

Publication status | Published - Aug 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Algebra and Number Theory