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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2601.20543 |
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| _version_ | 1866917349454512128 |
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| author | Yang, Hsin-Yi |
| author_facet | Yang, Hsin-Yi |
| contents | For any prime $p>0$, we prove that simple superspecial abelian surfaces over $\mathbb{F}_{p}$ admit CM liftings after base change at most to $\mathbb{F}_{p^2}$, by using the residual reflex condition (RRC) and Lie types. The CM-liftability of ordinary simple abelian surfaces is proved by Serre-Tate, and the CM-liftability of almost ordinary simple abelian surfaces is proved by Oswal-Shankar and Bergström-Karemaker-Marseglia, respectively. As there can only be ordinary, almost ordinary, or supersingular simple abelian surfaces over $\mathbb{F}_{p}$, our work is another step to complete the CM-liftability of simple abelian surfaces over $\mathbb{F}_{p}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20543 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | CM-liftability of simple superspecial abelian surfaces over prime fields Yang, Hsin-Yi Number Theory 11G10, 14K05, 14K22, 14K15, 14G17 For any prime $p>0$, we prove that simple superspecial abelian surfaces over $\mathbb{F}_{p}$ admit CM liftings after base change at most to $\mathbb{F}_{p^2}$, by using the residual reflex condition (RRC) and Lie types. The CM-liftability of ordinary simple abelian surfaces is proved by Serre-Tate, and the CM-liftability of almost ordinary simple abelian surfaces is proved by Oswal-Shankar and Bergström-Karemaker-Marseglia, respectively. As there can only be ordinary, almost ordinary, or supersingular simple abelian surfaces over $\mathbb{F}_{p}$, our work is another step to complete the CM-liftability of simple abelian surfaces over $\mathbb{F}_{p}$. |
| title | CM-liftability of simple superspecial abelian surfaces over prime fields |
| topic | Number Theory 11G10, 14K05, 14K22, 14K15, 14G17 |
| url | https://arxiv.org/abs/2601.20543 |