On graded Lie algebras associated to once-punctured elliptic curves with complex multiplication
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914298172801024 |
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| author | Ishii, Shun |
| author_facet | Ishii, Shun |
| contents | We study a graded Lie algebra arising from the Galois action on the pro-$p$ fundamental group of a once-punctured elliptic curve with complex multiplication. Among other things, we provide a minimal generating set of the rationalized Lie algebra under suitable assumptions. The proof is based on a slight variant of the theory of weighted completion of profinite groups developed by Hain and Matsumoto. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00615 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On graded Lie algebras associated to once-punctured elliptic curves with complex multiplication Ishii, Shun Number Theory We study a graded Lie algebra arising from the Galois action on the pro-$p$ fundamental group of a once-punctured elliptic curve with complex multiplication. Among other things, we provide a minimal generating set of the rationalized Lie algebra under suitable assumptions. The proof is based on a slight variant of the theory of weighted completion of profinite groups developed by Hain and Matsumoto. |
| title | On graded Lie algebras associated to once-punctured elliptic curves with complex multiplication |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.00615 |