Neighborhood of vertices in the isogeny graph of principally polarized superspecial abelian surfaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914710222274560 |
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| author | Xu, Zheng Ouyang, Yi Zhou, Zijian |
| author_facet | Xu, Zheng Ouyang, Yi Zhou, Zijian |
| contents | For two supersingular elliptic curves $E$ and $E'$ defined over $\mathbb{F}_{p^2}$, let $[E \times E']$ be the superspecial abelian surface with the principal polarization $\{0\} \times E' + E \times \{0\}$. We determine local structure of the vertices $[E \times E']$ in the $(\ell, \ell)$-isogeny graph of principally polarized superspecial abelian surfaces where either $E$ or $E'$ is defined over $\mathbb{F}_p$. We also present a simple new proof of the main theorem in \cite{LOX20}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14963 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Neighborhood of vertices in the isogeny graph of principally polarized superspecial abelian surfaces Xu, Zheng Ouyang, Yi Zhou, Zijian Number Theory Algebraic Geometry For two supersingular elliptic curves $E$ and $E'$ defined over $\mathbb{F}_{p^2}$, let $[E \times E']$ be the superspecial abelian surface with the principal polarization $\{0\} \times E' + E \times \{0\}$. We determine local structure of the vertices $[E \times E']$ in the $(\ell, \ell)$-isogeny graph of principally polarized superspecial abelian surfaces where either $E$ or $E'$ is defined over $\mathbb{F}_p$. We also present a simple new proof of the main theorem in \cite{LOX20}. |
| title | Neighborhood of vertices in the isogeny graph of principally polarized superspecial abelian surfaces |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2309.14963 |