A note on reductions of 2-dimensional crystalline Galois representations

Abstract

Let $p$ be an odd prime number, $K_f$ the finite unramified extension of ${\mathbb{Q}}_p$ of degree $f$, and $G_{K_f}$ its absolute Galois group. We construct analytic families of étale $(\phi ,\Gamma )$-modules which give rise to some families of 2-dimensional crystalline representations of $G_{K_f}$ with length of filtration $\ge p$. 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.

arXiv commentFinal version, to appear in Proc. A.M.S

References in corpus (2)

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