## Abstract

Let K = F _{q}(T). For a Drinfeld A-module φ of rank 2 defined over C _{∞}, there are an associated exponential function e _{φ} and lattice Λ _{φ} in C∞ given by uniformization over C _{∞}. We explicitly determine the Newton polygons of e _{φ} and the successive minima of Λ _{φ}. When φ is defined over K _{∞}, we give a refinement of Gardeyn's bounds for the action of wild inertia at ∞ on the torsion points of φ and a criterion for the lattice field to be unramified over K _{∞}. If φ is in addition defined over K, we make explicit Gardeyn's bounds for the action of wild inertia at finite primes on the torsion points of φ, using results of Rosen, and this gives an explicit bound on the degree of the different divisor of division fields of φ over K.

Original language | English |
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Pages (from-to) | 83-91 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 141 |

Issue number | 1 |

DOIs | |

State | Published - 2012 |

## Keywords

- Drinfeld modules
- Exponential functions
- Minimal bases
- Newton polygons