Quelques remarques à propos d'un théorème de Checcoli

1 Théorie des nombres et géométrie arithmétique
LMNO - Laboratoire de Mathématiques Nicolas Oresme
Abstract : In his thesis, S. Checcoli shows that, among other results, if $K$ is a number field and if $L/K$ is an infinite Galois extension with Galois group $G$ of finite exponent, then $L$ has uniformly bounded local degrees at every prime of $K$. In this article we gather two remarks about the generalisation of S. Checcoli's result to function fields of positive characteristic. We first show an analogue of her theorem $2.2.2$ in this context, under the hypothesis that the Galois group exponent is prime to $p$. Using an example, we then show that this hypothesis is in fact necesary.
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• HAL Id : hal-01052528, version 1
• ARXIV : 1408.3422

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Hugues Bauchère. Quelques remarques à propos d'un théorème de Checcoli. 2014. ⟨hal-01052528⟩

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