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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.00281 |
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| _version_ | 1866909818130792448 |
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| author | Qian, Lie |
| author_facet | Qian, Lie |
| contents | We describe the set of points of the trianguline variety over a given local Galois representation. Global analogues describing companion points in eigenvariety by [Bre14] and [HN17], can be thought of as a rational analogue to the weight part of Serre's conjecture. Along the same line, local companion points conjecture can be thought of as a rational analogue of attaching Serre weights to residual Galois representations. [BHS19] proves the conjecture assuming the given Galois representation is cristalline regular. We prove the conjecture in general cases only assuming some regularity conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00281 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Local Companion Points Conjecture Qian, Lie Number Theory We describe the set of points of the trianguline variety over a given local Galois representation. Global analogues describing companion points in eigenvariety by [Bre14] and [HN17], can be thought of as a rational analogue to the weight part of Serre's conjecture. Along the same line, local companion points conjecture can be thought of as a rational analogue of attaching Serre weights to residual Galois representations. [BHS19] proves the conjecture assuming the given Galois representation is cristalline regular. We prove the conjecture in general cases only assuming some regularity conditions. |
| title | The Local Companion Points Conjecture |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.00281 |