An Observation on the Cyclicity of the Group of the $\mathbb{F}_p$-Rational Points of Abelian Surfaces

Yamauchi, Takuya

Japan J. Indust. Appl. Math., Tome 24 (2007) no. 1, p. 307-318 / Harvested from Project Euclid

Résumé

Let $A$ be a principally polarized Abelian surface defined over $\mathbb{Q}$ with $\End(A)=\mathbb{Z}$ and $\widetilde{A}$ be the reduction at a good prime $p$. In this paper, we study the density of prime numbers $p$ for which $\widetilde{A}(\mathbb{F}_p)$ is a cyclic group and establish a conjecture which relates this density.

Publié le : 2007-10-14
Classification: Abelian surface, cyclicity

@article{1197909115,
     author = {Yamauchi, Takuya},
     title = {An Observation on the Cyclicity of the Group of the $\mathbb{F}\_p$-Rational Points of Abelian Surfaces},
     journal = {Japan J. Indust. Appl. Math.},
     volume = {24},
     number = {1},
     year = {2007},
     pages = { 307-318},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1197909115}
}

Yamauchi, Takuya. An Observation on the Cyclicity of the Group of the $\mathbb{F}_p$-Rational Points of Abelian Surfaces. Japan J. Indust. Appl. Math., Tome 24 (2007) no. 1, pp.  307-318. http://gdmltest.u-ga.fr/item/1197909115/