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arXiv · 1202.5711

A note on reductions of 2-dimensional crystalline Galois representations

Gerasimos Dousmanis
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Abstract

Let $p$ be an odd prime number, $K_{f}$ the finite unramified extension of $\mathbb{Q}_{p}$ of degree $f$, and $G_{K_{f}}$ its absolute Galois group. We construct analytic families of étale $(φ,Γ)$-modules which give rise to some families of 2-dimensional crystalline representations of $G_{K_{f}}$ with length of filtration $\geq p$. As an application, we prove that the modulo $p$ reductions of the members of each such family (with respect to appropriately chosen Galois-stable lattices) are constant.

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Gerasimos Dousmanis. 2013-02-09. A note on reductions of 2-dimensional crystalline Galois representations. https://arxiv.org/abs/1202.5711

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