Construction de représentations p-adiques semi-stables

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 ...

Formes Modulaires Et Représentations -adiques

(2π)Γ(s)Lτ (s) is invariant under s 7→ 12 − s. The Ramanujan conjecture affirms that the roots of the polynomial Hp are of absolute value p −11/2 (i.e. that |τ(p)| < 2p). These properties, proven or conjectural, are similar to conjectural properties of zeta functions of algebraic varieties over Q. Suggested by this, in a first approximation, it is tempting to interpret the function Lτ as the ze...

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). ...

F p-représentations semi-stables

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