Potentially crystalline deformation rings and Serre weight conjectures: shapes and shadows
Résumé
We prove the weight part of Serre's conjecture in generic situations for forms of U (3) which are compact at infinity and split at places dividing p as conjectured by [Her09]. We also prove automorphy lifting theorems in dimension three. The key input is an explicit description of tamely potentially crystalline deformation rings with Hodge-Tate weights (2, 1, 0) for K/Qp unramified combined with patching techniques. Our results show that the (geometric) Breuil-Mézard conjectures hold for these deformation rings.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
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