Serre weight conjectures for $\mathrm{GSp}_4$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914077568139264 |
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| author | Le, Daniel Hung, Bao V. Le Lee, Heejong |
| author_facet | Le, Daniel Hung, Bao V. Le Lee, Heejong |
| contents | We prove the weight part of Serre's conjecture for Galois representations valued in $\mathrm{GSp}_4$ that are tamely ramified with explicit genericity at places above $p$ as conjectured by Herzig--Tilouine and Gee--Herzig--Savitt. This improves on arXiv:2304.13879 where an inexplicit genericity hypothesis was required. As an application, we prove a modularity lifting theorem for $\mathrm{GSp}_4$ under similar assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Serre weight conjectures for $\mathrm{GSp}_4$ Le, Daniel Hung, Bao V. Le Lee, Heejong Number Theory We prove the weight part of Serre's conjecture for Galois representations valued in $\mathrm{GSp}_4$ that are tamely ramified with explicit genericity at places above $p$ as conjectured by Herzig--Tilouine and Gee--Herzig--Savitt. This improves on arXiv:2304.13879 where an inexplicit genericity hypothesis was required. As an application, we prove a modularity lifting theorem for $\mathrm{GSp}_4$ under similar assumptions. |
| title | Serre weight conjectures for $\mathrm{GSp}_4$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.04805 |