Polygones de Hodge, de Newton et de l'inertie modérée des représentations semi-stables

Xavier Caruso (1) , David Savitt (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Mathematics [University of Arizona]

Let k be a perfect field, and K be a totally ramified extension of K_0 = Frac W(k) of degree e. To a semi-stable p-adic representation of G_K (the absolute Galois group of K), one can classicaly associate two polygons : the Hodge polygon et the Newton polygon. It is well known that the former lies below the latter, and that they have same endpoints. In this note, we introduce a third polygon gotten from the semi-simplification of the representation mod p, and, under some conditions on Hodge-Tate weights, we prove that it lies above the Hodge polygon again with same endpoint. We finally examine one exemple associated to a crystalline representation.

Mots clés: Représentations semi-stables; Réseaux

Domaines: Théorie des nombres [math.NT]

Xavier Caruso, David Savitt. Polygones de Hodge, de Newton et de l'inertie modérée des représentations semi-stables. Mathematische Annalen, 2009, 343 (4), pp.773-789. ⟨10.1007/s00208-008-0289-1⟩. ⟨hal-00211173v2⟩