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arXiv 2002.04420math.NT
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关于$\mathbb{F}_p$上阿贝尔簇个数的下界

On the lower bound of the number of abelian varieties over $\mathbb{F}_p$

Jungin Lee

备注：
20 pages, to appear in IMRN
发表信息：
International Mathematics Research Notices (2022), no. 6, 4290-4317
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摘要：

本文证明了维数为$g$的素域$\mathbb{F}_p$上的阿贝尔簇的同构类的个数$B(p,g)$有一个下界$p^{\frac{1}{2} g^2 (1+o(1))}$为$g \rightarrow \infty$ .这是关于$B(p,g)$的下界的第一个非平凡结果。我们还将Lipnowski和Tsimerman给出的$B(p,g)$的上限$2^{34g^2} p^{\frac{69}{4} g^2 (1+o(1))}$（Duke Math. J. 167：3403-3453，2018）改进为$p^{\frac{45}{4} g^2(1+o(1))}$。

英文摘要：

In this paper, we prove that the number $B(p,g)$ of isomorphism classes of abelian varieties over a prime field $\mathbb{F}_p$ of dimension $g$ has a lower bound $p^{\frac{1}{2} g^2 (1+o(1))}$ as $g \rightarrow \infty$. This is the first nontrivial result on the lower bound of $B(p,g)$. We also improve the upper bound $2^{34g^2} p^{\frac{69}{4} g^2 (1+o(1))}$ of $B(p,g)$ given by Lipnowski and Tsimerman (Duke Math. J. 167:3403-3453, 2018) to $p^{\frac{45}{4} g^2(1+o(1))}$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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