论文标题
在$ \ mathbb {f} _p $上方的阿贝尔品种数量的下限
On the lower bound of the number of abelian varieties over $\mathbb{F}_p$
论文作者
论文摘要
在本文中，我们证明了数字$ b（p，g）$的同构$类别的阿贝利亚品种在prime字段上$ \ mathbb {f} _p {dimension $ g $具有下限$ p^{\ frac {\ frac {1} {2} {2} {2} g^2（1+O（1+O（1+O（1+O（1+O（1+O（1+O），这是$ b（p，g）$的下限的第一个非平地结果。我们还改善了上限$ 2^{34g^2} p^{\ frac {69} {4} g^2（1+o（1）} $ $ b（p，g）$ of lipnowski and tsimerman和tsimerman（p，g）$，由MATH。 g^2（1+o（1））} $。
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 $p^{\frac{45}{4} g^2(1+o(1))}$.
