Reduction modulo p of two-dimensional crystalline representations of G_Qp of slope less than three

2015/03/28 by Bodan Arsovski, Arsovski, Bodan
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1503.08309

arxiv created 2015/05/18 · arxiv updated 2015/05/19

Abstract

We use the p-adic local Langlands correspondence for GL₂(Q_p) to find the reduction modulo p of certain two-dimensional crystalline Galois representations. In particular, we resolve a conjecture of Breuil, Buzzard, and Emerton in the case when the slope is strictly between one and three, and prove partial results towards this conjecture for arbitrary slopes. Moreover, we partially classify the reduction modulo p of these representations when the slope is equal to one.

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