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arXiv · 2104.09761

Potential Automorphy for $GL_n$

Lie Qian
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Abstract

We prove potential automorphy results for a single Galois representation $G_F \rightarrow GL_n(\overline{\mathbb{Q}}_l)$ where $F$ is a CM number field. The strategy is to use the $p,q$ switch trick and modify the Dwork motives employed in \cite{HSBT} to break self-duality of the motives, but not the Hodge-Tate weights. Another key result to prove is the ordinarity of certain $p$-adic representations, which follows from log geometry techniques. One input is the automorphy lifting theorem in \cite{tap}.

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Lie Qian. 2021-04-20. Potential Automorphy for $GL_n$. https://arxiv.org/abs/2104.09761

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