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Fonctorialité, idéaux de congruence et grandes images de représentations galoisiennes associées aux familles de Hida

Abstract : Hida has studied the image of Galois representation associated to a p-adic Hida family of automorphic forms. He has proved that the image of a non-CM family ofordinary classic modular forms contains a congruence subgroup. He also related the optimal level of congruence subgroup to the congruence ideal between the non-CM Hida family and the CM ones. This thesis is divided into two parts. In the first part,we generalize this type of results to ordinary Hida families over reductive groups under some technical hypothesis. In the second part, we consider concrete cases. We prove that the technical hypothesis are satised for these cases. Hence the same type of results is established automatically.
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Submitted on : Friday, November 9, 2018 - 9:49:05 AM
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Huan Chen. Fonctorialité, idéaux de congruence et grandes images de représentations galoisiennes associées aux familles de Hida. Théorie des nombres [math.NT]. Université Sorbonne Paris Cité, 2017. Français. ⟨NNT : 2017USPCD040⟩. ⟨tel-01917067⟩

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