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arXiv · 1509.04979

Crystalline lifts of two-dimensional mod $p$ automorphic Galois representations

Fred Diamond·Davide A. Reduzzi
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Abstract

We show that a sufficient condition for an irreducible automorphic Galois representation $\rho: G_F\to\mathrm{GL}_2({\overline{{\bf F}}_p})$ of a totally real field $F$ to have an automorphic crystalline lift is that for each place $v$ of $F$ above $p$ the restriction $\mathrm{det}\rho|_{I_v}$ is a fixed power of the mod $p$ cyclotomic character. Moreover, we show that the only obstruction to controlling the level and character of such automorphic lifts arises for badly dihedral representations.

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Fred Diamond, Davide A. Reduzzi. 2015-09-16. Crystalline lifts of two-dimensional mod $p$ automorphic Galois representations. https://doi.org/10.4310/mrl.2018.v25.n1.a3

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