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arXiv · 2309.14963

Neighborhood of vertices in the isogeny graph of principally polarized superspecial abelian surfaces

Zheng Xu·Yi Ouyang·Zijian Zhou
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Abstract

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}.

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Zheng Xu, Yi Ouyang, Zijian Zhou. 2023-09-26. Neighborhood of vertices in the isogeny graph of principally polarized superspecial abelian surfaces. https://arxiv.org/abs/2309.14963

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