Limites de représentations cristallines

Laurent Berger (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We provide an answer to two questions of Fontaine (in the unramified case). First, we show that a limit of crystalline representations, of bounded Hodge-Tate weights, is itself crystalline. Second, we show that every admissible filtered $\phi$-module "comes from" a $(\phi,\Gamma)$-module of finite q-height.

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Laurent Berger. Limites de représentations cristallines. Compositio Mathematica, 2004, 140, pp.1473--1498. ⟨hal-00575499⟩