On differential modules associated to de Rham representations in the imperfect residue field case

الأصل · EN

Let K be a complete discrete valuation field of mixed characteristic (0,p), whose residue field may not be perfect, and Gₖ the absolute Galois group of K. In the first part of this paper, we prove that Scholl's generalization of fields of norms over K is compatible with Abbes-Saito's ramification theory. In the second part, we construct a functor NdR(V) associating a de Rham representation V with a (φ,∇)-module in the sense of Kedlaya. Finally, we prove a compatibility between Kedlaya's differential Swan conductor of NdR(V) and Swan conductor of V, which generalizes Marmora's formula.