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

Fuente: arXiv
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Main Author: Matsumoto, Kojiro
Format: Preprint
Published: 2023
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author Matsumoto, Kojiro
author_facet Matsumoto, Kojiro
contents 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 $\mathrm{GL}_2(\mathbb{A}_F )$.
format Preprint
id arxiv_https___arxiv_org_abs_2312_01551
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On the potential automorphy and the local-global compatibility for the monodromy operators at $p \neq l$ over CM fields
Matsumoto, Kojiro
Number Theory
Representation Theory
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 $\mathrm{GL}_2(\mathbb{A}_F )$.
title On the potential automorphy and the local-global compatibility for the monodromy operators at $p \neq l$ over CM fields
topic Number Theory
Representation Theory
url https://arxiv.org/abs/2312.01551