Reductions of Some Two-Dimensional Crystalline Representations via Kisin Modules

We determine rational Kisin modules associated with 2-dimensional, irreducible, crystalline representations of Gal(Qp/Qp) of Hodge Tate weights 0, k-1. If the slope is larger than k-1 p, we further identify an integral Kisin module, which we use to calculate the semisimple reduction of the Galois representation. In that range, we find that the reduction is constant, thereby improving on a theorem of Berger, Li, and Zhu.