On ordinary isogeny graphs with level structure
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914865727143936 |
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| author | Lei, Antonio Müller, Katharina |
| author_facet | Lei, Antonio Müller, Katharina |
| contents | Let $l$ and $p$ be two distinct prime numbers. We study $l$-isogeny graphs of ordinary elliptic curves defined over a finite field of characteristic $p$, together with a level structure. Firstly, we show that as the level varies over all $p$-powers, the graphs form an Iwasawa-theoretic abelian $p$-tower, which can be regarded as a graph-theoretical analogue of the Igusa tower of modular curves. Secondly, we study the structure of the crater of these graphs, generalizing previous results on volcano graphs. Finally, we solve an inverse problem of graphs arising from the crater of $l$-isogeny graphs with level structures, partially generalizing a recent result of Bambury, Campagna and Pazuki. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10981 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On ordinary isogeny graphs with level structure Lei, Antonio Müller, Katharina Number Theory 5C25, 11G20 Let $l$ and $p$ be two distinct prime numbers. We study $l$-isogeny graphs of ordinary elliptic curves defined over a finite field of characteristic $p$, together with a level structure. Firstly, we show that as the level varies over all $p$-powers, the graphs form an Iwasawa-theoretic abelian $p$-tower, which can be regarded as a graph-theoretical analogue of the Igusa tower of modular curves. Secondly, we study the structure of the crater of these graphs, generalizing previous results on volcano graphs. Finally, we solve an inverse problem of graphs arising from the crater of $l$-isogeny graphs with level structures, partially generalizing a recent result of Bambury, Campagna and Pazuki. |
| title | On ordinary isogeny graphs with level structure |
| topic | Number Theory 5C25, 11G20 |
| url | https://arxiv.org/abs/2306.10981 |