Construction of some families of 2-dimensional crystalline representations

Laurent Berger (1) , Hanfeng Li (2) , Hui June Zhu (2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 Department of Mathematics [Buffalo]

We construct explicitly some analytic families of etale (phi,Gamma)-modules, which give rise to analytic families of 2-dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on the reduction modulo p of those representations, and extend some results (of Deligne, Edixhoven, Fontaine and Serre) on the representations arising from modular forms.

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

Laurent Berger, Hanfeng Li, Hui June Zhu. Construction of some families of 2-dimensional crystalline representations. Mathematische Annalen, 2004, 329, pp.365--377. ⟨hal-00575495⟩