Euler characteristics of the generalized Kloosterman sheaves for symplectic and orthogonal groups
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914891139383296 |
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| author | Fu, Yu Gu, Miao Pam |
| author_facet | Fu, Yu Gu, Miao Pam |
| contents | We study the monodromy of certain $\ell$-adic local systems attached to the generalized Kloosterman sheaves constructed by Yun and calculate their Euler characteristics under standard representations in the cases of symplectic and split/quasi-split orthogonal groups. This provides evidence for the conjectural description of their Swan conductors at $\infty$ which is predicted by Reeder-Yu on the Langlands parameters attached to the epipelagic representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Euler characteristics of the generalized Kloosterman sheaves for symplectic and orthogonal groups Fu, Yu Gu, Miao Pam Number Theory Algebraic Geometry Representation Theory 14D24, 22E57 (Primary) 11F70, 11L05 (Secondary) We study the monodromy of certain $\ell$-adic local systems attached to the generalized Kloosterman sheaves constructed by Yun and calculate their Euler characteristics under standard representations in the cases of symplectic and split/quasi-split orthogonal groups. This provides evidence for the conjectural description of their Swan conductors at $\infty$ which is predicted by Reeder-Yu on the Langlands parameters attached to the epipelagic representations. |
| title | Euler characteristics of the generalized Kloosterman sheaves for symplectic and orthogonal groups |
| topic | Number Theory Algebraic Geometry Representation Theory 14D24, 22E57 (Primary) 11F70, 11L05 (Secondary) |
| url | https://arxiv.org/abs/2407.19700 |