Algèbres $L^1$ $p$-adiques

Anneaux de Fonctions p-adiques

We study first-order properties of the quotient rings 9(V)/1 by a prime ideal 9, where 9( V) is the ring of p-adic valued continuous definable functions on some affine p-adic variety V. We show that they are integrally closed Henselian local rings, with a p-adically closed residue field and field of fractions, and they are not valuation rings in general but always satisfy Vx, y(x Iy2 V y IX2). ...

Représentations P-adiques Et Normes Universelles

Let V be a crystalline p-adic representation of the absolute Galois group GK of an finite unramified extension K of Qp and T a lattice of V stable by GK . We prove the following result : Let FilV be the maximal sub-representation of V with Hodge-Tate weights strictly positive and FilT = T ∩ FilV . Then, the projective limit of the H g (K(μpn), T ) is equal up to torsion to the projective limit ...

Irrégularité et Conducteur de Swan p - adiques

Let V be a de-Rham representation of the Galois group of a local field of mixed characteristic (0, p). We relate the Swan conductor of the associated Weil-Deligne representation to the irregularity of the corresponding p-adic differential equation. 2000 Mathematics Subject Classification: 11F80,11F85,11S15,12H25

Classification des séries discrètes pour certains groupes classiques p-adiques

Définissabilité dans les Corps de Fonctions p-Adiques

We study function fields over p-adically closed fields in the first-order language of fields. Using ideas of Duret [D], we show that the field of constants is definable, and that the genus is an elementary property. ?0. Introduction. Soit p un nombre premier fixed. Un corps p-adiquement clos est un corps elementairement equivalent au corps des nombres p-adiques, Qp. Le langage des corps sera le...