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arXiv · 2312.01551

On the potential automorphy and the local-global compatibility for the monodromy operators at $p \neq l$ over CM fields

Kojiro Matsumoto
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Abstract

Let $F$ be a CM field. In this paper, we prove the local-global compatibility for cohomological cuspidal automorphic representations of $\mathrm{GL}_n(\mathbb{A}_F)$ at $p \neq l$ by using certain potential automorphy theorems in some cases including higher dimensional cases. Moreover, we also prove the Ramanujan conjecture for cohomological cuspidal automorphic representations of $\mathrm{GL}_2(\mathbb{A}_F )$.

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Kojiro Matsumoto. 2023-12-04. On the potential automorphy and the local-global compatibility for the monodromy operators at $p \neq l$ over CM fields. https://arxiv.org/abs/2312.01551

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