"Reductions of Some Two-Dimensional Crystalline Representations via Kisin Modules"
Authors: Bergdall, John; Levin, Brandon
Source: International Mathematics Research Notices, Volume 2022, Issue 4, Pages 3170–3197, Article Number: rnaa240, DOI: 10.1093/imrn/rnaa240, February 2022
Type of Publication: Article
Abstract: We determine rational Kisin modules associated with 2-dimensional, irreducible, crystalline representations of the absolute Galois group of the p-adic numbers whose Hodge-Tate weights are 0 and 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.