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Interprétation p-automatique des groupes formels le Lubin-Tate et des modules de Drinfeld réduits

Abstract : This work is firstly based on the observation of a result by P. Robba which states, for any p-adic integer λ, the equivalence between the rationality of λ and the algebraicity of (1+T)λ mod p ∈ Fp[[T]] over Fp(T). As this power series is before reduction essentially the same as the endomorphism [λ](T) of the multiplicative group over Zp we generalize this result to a class of LubinTate formal groups whose logarithm satisfies a certain condition of algebraicity Then we interpret the result by means of the Fontaine Wintenberger's fonctor XK and draw consequences about algebraic independence of automorphisms of local fields. In the second part of this work we establish the analogue of the Robba's theorem in the context of Drinfeld modules of rank 1 defined on the P-adic completion Fq[t]P of Fq[t] where P is a monic prime polynomial over Fq with degree n.
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https://tel.archives-ouvertes.fr/tel-00474315
Contributor : Yolande Vieceli <>
Submitted on : Thursday, April 22, 2010 - 1:45:55 PM
Last modification on : Thursday, January 11, 2018 - 6:12:25 AM
Long-term archiving on: : Tuesday, September 28, 2010 - 12:55:50 PM

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  • HAL Id : tel-00474315, version 1

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Christophe Cadic. Interprétation p-automatique des groupes formels le Lubin-Tate et des modules de Drinfeld réduits. Mathématiques [math]. Université de Limoges, 1999. Français. ⟨tel-00474315⟩

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