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arXiv · 2104.14732

Modularity of $\operatorname{PGL}_2(\mathbb{F}_p)$-representations over totally real fields

Patrick B. Allen·Chandrashekhar B. Khare·Jack A. Thorne
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Abstract

We study an analogue of Serre's modularity conjecture for projective representations $\overlineρ: \operatorname{Gal}(\overline{K} / K) \rightarrow \operatorname{PGL}_2(k)$, where $K$ is a totally real number field. We prove new cases of this conjecture when $k = \mathbb{F}_5$ by using the automorphy lifting theorems over CM fields established in previous work of the authors.

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Patrick B. Allen, Chandrashekhar B. Khare, Jack A. Thorne. 2021-09-09. Modularity of $\operatorname{PGL}_2(\mathbb{F}_p)$-representations over totally real fields. https://doi.org/10.1073/pnas.2108064118

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