On the potential automorphy and the local-global compatibility for the monodromy operators at $p \neq l$ over CM fields
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915644175286272 |
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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 |