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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.16639 |
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| _version_ | 1866910423265050624 |
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| author | Zhang, Xiaoyu Zhao, Heer |
| author_facet | Zhang, Xiaoyu Zhao, Heer |
| contents | In this article we study the Honda-Tate theory for log abelian varieties over an fs log point $S=(\mathrm{Spec}(\mathbf{k}),M_S)$ for $\mathbf{k}=\mathbb{F}_q$ a finite field, generalizing the classical Honda-Tate theory for abelian varieties over $\mathbf{k}$. For the standard log point $S$, we give a complete description of the isogeny classes of such log abelian varieties using Weil $q$-numbers of weight 0,1, and 2. In the general case where $M_S$ admits a global chart $P\to\mathbf{k}$ with $P=\mathbb{N}^k$, we also give a complete description of simple isogeny classes of log abelian varieties over $S$ in terms of rational points in generalized simplices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16639 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Honda-Tate theory for log abelian varieties over finite fields Zhang, Xiaoyu Zhao, Heer Number Theory 14A21 (primary), 14K02, 11G99 (secondary) In this article we study the Honda-Tate theory for log abelian varieties over an fs log point $S=(\mathrm{Spec}(\mathbf{k}),M_S)$ for $\mathbf{k}=\mathbb{F}_q$ a finite field, generalizing the classical Honda-Tate theory for abelian varieties over $\mathbf{k}$. For the standard log point $S$, we give a complete description of the isogeny classes of such log abelian varieties using Weil $q$-numbers of weight 0,1, and 2. In the general case where $M_S$ admits a global chart $P\to\mathbf{k}$ with $P=\mathbb{N}^k$, we also give a complete description of simple isogeny classes of log abelian varieties over $S$ in terms of rational points in generalized simplices. |
| title | Honda-Tate theory for log abelian varieties over finite fields |
| topic | Number Theory 14A21 (primary), 14K02, 11G99 (secondary) |
| url | https://arxiv.org/abs/2404.16639 |