Reductions of -Dimensional Semistable Representations With Large -Invariant

Abstract

We determine reductions of $2$ -dimensional, irreducible, semistable, and non-crystalline representations of $\mathrm {Gal}\left (\overline {\mathbb {Q}}_p/\mathbb {Q}_p\right )$ 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 $k \geq p$ .