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Uniformisation des variétés de Laumon-Rapoport-Stuhler et conjecture de Drinfeld-Carayol

Thomas Hausberger — 2005

Annales de l’institut Fourier

Considérons les variétés de “ $D$ -faisceaux elliptiques” $ℰ ℓ ℓ$ introduites par Laumon, Rapoport et Stuhler, définies sur un corps de fonctions $F$ d’une variable sur un corps fini, où $D$ est une algèbre de division de dimension $d^{2}$ sur $F$ . Nous montrons que ces variétés admettent, en une place $o$ de $F$ où $D_{o}$ est un corps gauche d’invariant $1 / d$ , une uniformisation rigide-analytique par l’espace de Drinfeld $Ω^{d}$ , ou par les revêtements $Σ_{n}^{d}$ de $Ω^{d}$ (selon la structure de niveau). Ce résultat constitue l’analogue du théorème...

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