Construction of some families of 2-dimensional crystalline representations

2003/10/17 by Laurent Berger, Hanfeng Li, Hui June Zhu · 2 citations
Mathematics · #math.NT #math.AG #msc:11F80 #msc:11F33 #msc:11F85 #msc:14F30

paper · pdf

published as Mathematische Annalen 329 (2004), no.2, 365-377. · 13 pages, english and french abstracts

arxiv created 2003/10/17 · arxiv updated 2009/12/01

Abstract

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.

Cited by

• On the growth of Tate-Shafarevich groups of p-supersingular abelian varieties of \rm GL₂-type over ℤ_p-extensions of number fields
• The residual monodromy for the Dwork family in even characteristic and its applications to Galois representations

Related

• A note on reductions of 2-dimensional crystalline Galois representations
• On reductions of families of crystalline Galois representations
• Crystalline representations of G_Qp^a with coefficients
• Sur la réduction des représentations cristallines de dimension 2 en poids moyens
• Moduli stacks of étale (phi,Gamma)-modules and the existence of crystalline lifts