A Rank-Two Case of Local-Global Compatibility for $l = p$
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910514133598208 |
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| author | Yang, Yuji |
| author_facet | Yang, Yuji |
| contents | We prove the classical $l = p$ local-global compatibility conjecture for certain regular algebraic cuspidal automorphic representations of weight 0 for GL$_2$ over CM fields. Using an automorphy lifting theorem, we show that if the automorphic side comes from a twist of Steinberg at $v | l$, then the Galois side has nontrivial monodromy at $v$. Based on this observation, we will give a definition of the Fontaine-Mazur $\mathcal{L}$-invariants attached to certain automorphic representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00288 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Rank-Two Case of Local-Global Compatibility for $l = p$ Yang, Yuji Number Theory We prove the classical $l = p$ local-global compatibility conjecture for certain regular algebraic cuspidal automorphic representations of weight 0 for GL$_2$ over CM fields. Using an automorphy lifting theorem, we show that if the automorphic side comes from a twist of Steinberg at $v | l$, then the Galois side has nontrivial monodromy at $v$. Based on this observation, we will give a definition of the Fontaine-Mazur $\mathcal{L}$-invariants attached to certain automorphic representations. |
| title | A Rank-Two Case of Local-Global Compatibility for $l = p$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2407.00288 |