Construction of some families of 2-dimensional crystalline representations

By Laurent Berger, Hanfeng Li, Hui June Zhu. 2003

123 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/05242b6976158eb5fb1ab203a97661c7d118187e

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Euler systems for Rankin–Selberg convolutions of modular forms (2012, methodology): “In the nonordinary case one reasons similarly using the description of the Wach module of the (unique up to scaling) lattice in Dcris(VLp(g)) given in [BLZ04].”
A Local-Global Compatibility Conjecture in the p-adic Langlands Programme for GL 2/Q (2006, background): “Condition (5) has been verified by Berger [5] (improving on earlier results of various authors [7, 9, 10, 15]).”
Coleman maps and the p-adic regulator (2010, methodology): “When vp(ap) is sufficiently large, we make use of the basis of N(V ) constructed in [Berger et al. 2004] to show that the first Coleman map is surjective under some additional technical conditions.”
On Serre's conjecture for 2-dimensional mod p representations of Gal( Q=Q) (2009, unknown): “of [4].”