Reductions of some two-dimensional crystalline representations via Kisin\n modules

2019/08/23 by John Bergdall, Bergdall, John, Brandon Levin +1 · 2 citations
Mathematics · #11F80 (11F85) #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1908.09036

openalex publication_date 2019/08/23 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We determine rational Kisin modules associated with two-dimensional,\nirreducible, crystalline representations of\n\Gal(\\ℚ_p/\ℚ_p) of Hodge-Tate weights 0,\nk-1. If the slope is larger than lfloor \(k-1)/(p) rfloor, we further\nidentify an integral Kisin module, which we use to calculate the semisimple\nreduction of the Galois representation. In that range, we find that the\nreduction is constant, thereby improving on a theorem of Berger, Li, and Zhu.\n

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