A note on reductions of 2-dimensional crystalline Galois representations

2012/02/26 by Gerasimos Dousmanis, Dousmanis, Gerasimos
Mathematics · #11F80 #11F85 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1202.5711

openalex publication_date 2012/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be an odd prime number, K_f the finite unramified extension of ℚ_p of degree f, and G_K_f 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 G_K_f 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.

Citations

• Limites de représentations cristallines
• The Buzzard-Diamond-Jarvis conjecture for unitary groups

Related

• On reductions of families of crystalline Galois representations
• Reductions of Some Crystalline Representations in the Unramified Setting
• Construction of some families of 2-dimensional crystalline representations
• Crystalline representations of G_Qp^a with coefficients
• Reductions of Crystalline Representations for Small Weights