, Volume 329, Issue 2, pp 365-377
Date: 13 Mar 2004

Construction of some families of 2-dimensional crystalline representations

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Abstract.

We construct explicitly some analytic families of étale (φ,Γ)-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.

Mathematics Subject Classification (2000): 11F80, 11F33, 11F85, 14F30