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On the Lower Bound of the Number of Abelian Varieties Over 𝔽p
- Source :
- International Mathematics Research Notices. 2022:4290-4317
- Publication Year :
- 2020
- Publisher :
- Oxford University Press (OUP), 2020.
-
Abstract
- 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 1st 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 [ 7] to $p^{\frac{45}{4} g^2(1+o(1))}$.
Details
- ISSN :
- 16870247 and 10737928
- Volume :
- 2022
- Database :
- OpenAIRE
- Journal :
- International Mathematics Research Notices
- Accession number :
- edsair.doi...........98bb53c3b5e8a9a87ce6d06257c58a32