Isogeny classes of non-simple abelian surfaces over finite fields

Yu Fu

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arXiv · 2308.11132

Isogeny classes of non-simple abelian surfaces over finite fields

Yu Fu

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Abstract

Let $A=E \times E_{ss}$ be a principally polarized almost ordinary split abelian surface over a finite field $\mathbb{F}_{q}$. We give asymptotic upper and lower bounds on the number of principally polarized abelian surfaces over $\mathbb{F}_{q^{n}}$ that are $\overline{\mathbb{F}}_{q}$-isogenous to $A$ up to isomorphism, which is a refinement of the results in the work of Achter and Howe.

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BibTeX RIS

Yu Fu. 2023-08-22. Isogeny classes of non-simple abelian surfaces over finite fields. https://arxiv.org/abs/2308.11132

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