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The goal of this paper is to study certain -adic differential operators on automorphic forms on . These operators are a generalization to the higher-dimensional, vector-valued situation of the -adic differential operators constructed for Hilbert modular forms by N. Katz. They are a generalization to the -adic case of the -differential operators first studied by H. Maass and later studied extensively by M. Harris and G. Shimura. The operators should be useful in the construction of certain -adic...
Soient et deux nombres premiers distincts et le quotient de la courbe de Shimura de discriminant par l’involution d’Atkin-Lehner . Nous décrivons un moyen permettant de vérifier un critère de Parent et Yafaev en grande généralité pour prouver que si et satisfont des conditions de congruence explicites, connues comme les conditions du cas non ramifié de Ogg, et si est assez grand par rapport à , alors le quotient n’a pas de point rationnel non spécial.
Let be a field of characteristic . Let be a over (i.e., an -truncated Barsotti–Tate group over ). Let be a -scheme and let be a over . Let be the subscheme of which describes the locus where is locally for the fppf topology isomorphic to . If , we show that is pure in , i.e. the immersion is affine. For , we prove purity if satisfies a certain technical property depending only on its -torsion . For , we apply the developed techniques to show that all level ...
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