Reductions of 2-dimensional semi-stable representations with large \mathcal L-invariant

2020/06/29 by Bergdall, John, Levin, Brandon, Liu, Tong
#11F80 (11F85) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.16294

Abstract

We determine reductions of 2-dimensional, irreducible, semi-stable, and non-crystalline representations of Gal(\mathbb Q_p/\mathbb Q_p) with Hodge--Tate weights 0 < k-1 and with \mathcal L-invariant whose p-adic norm is sufficiently large, depending on k. Our main result provides the first systematic examples of the reductions for k ≥ p.

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