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Faculty Publication: Assistant Professor of Mathematics John Bergdall

March 18, 2022

"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.

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