On possibilities of 3-adic Galois images associated to isogeny-torsion graphs
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916884427833344 |
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| author | Rakvi |
| author_facet | Rakvi |
| contents | Let $E$ be a non CM elliptic curve defined over $\Q$. There is an isogeny-torsion graph associated to $E$ and there is also a Galois representation $ρ_{E,l^{\infty}} \colon \Gal(\Qbar/\Q) \to \GL_2(\ZZ_{\ell})$ associated to $E$ for every prime $\ell.$ In this article, we explore the relation between these two objects when $\ell=3$. More precisely, we give a classification of 3-adic Galois images associated to vertices of the isogeny-torsion graph of $E.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_04074 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On possibilities of 3-adic Galois images associated to isogeny-torsion graphs Rakvi Number Theory Let $E$ be a non CM elliptic curve defined over $\Q$. There is an isogeny-torsion graph associated to $E$ and there is also a Galois representation $ρ_{E,l^{\infty}} \colon \Gal(\Qbar/\Q) \to \GL_2(\ZZ_{\ell})$ associated to $E$ for every prime $\ell.$ In this article, we explore the relation between these two objects when $\ell=3$. More precisely, we give a classification of 3-adic Galois images associated to vertices of the isogeny-torsion graph of $E.$ |
| title | On possibilities of 3-adic Galois images associated to isogeny-torsion graphs |
| topic | Number Theory |
| url | https://arxiv.org/abs/2307.04074 |