A note on reductions of 2-dimensional crystalline Galois representations

الأصل · EN

Let p be an odd prime number, Kf the finite unramified extension of Qₚ of degree f, and GKf its absolute Galois group. We construct analytic families of étale (φ,Γ)-modules which give rise to some families of 2-dimensional crystalline representations of GKf with length of filtration ≥ p. As an application, we prove that the modulo p reductions of the members of each such family (with respect to appropriately chosen Galois-stable lattices) are constant.