Isogeny classes of non-simple abelian surfaces over finite fields
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909748034535424 |
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| author | Fu, Yu |
| author_facet | Fu, Yu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11132 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Isogeny classes of non-simple abelian surfaces over finite fields Fu, Yu Number Theory 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. |
| title | Isogeny classes of non-simple abelian surfaces over finite fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2308.11132 |