Isogeny graphs with level structures arrising from the Verschiebung map
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929663776915456 |
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| author | Lei, Antonio Müller, Katharina |
| author_facet | Lei, Antonio Müller, Katharina |
| contents | We enhance an isogeny graph of elliptic curves by incorporating level structures defined by bases of the kernels of iterates of the Verschiebung map. We extend several previous results on isogeny graphs with level structures defined by geometric points to these graphs. Firstly, we prove that these graphs form $\mathbb{Z}_p$-towers of graph coverings as the power of the Verschiebung map varies. Secondly, we prove that the connected components of these graphs display a volcanic structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03846 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isogeny graphs with level structures arrising from the Verschiebung map Lei, Antonio Müller, Katharina Number Theory Combinatorics 05C30, 11G20, 11R23, 11G17, 11K02 We enhance an isogeny graph of elliptic curves by incorporating level structures defined by bases of the kernels of iterates of the Verschiebung map. We extend several previous results on isogeny graphs with level structures defined by geometric points to these graphs. Firstly, we prove that these graphs form $\mathbb{Z}_p$-towers of graph coverings as the power of the Verschiebung map varies. Secondly, we prove that the connected components of these graphs display a volcanic structure. |
| title | Isogeny graphs with level structures arrising from the Verschiebung map |
| topic | Number Theory Combinatorics 05C30, 11G20, 11R23, 11G17, 11K02 |
| url | https://arxiv.org/abs/2501.03846 |