Mathematical Journal of Okayama University volume64 issue1
2022-01 発行

A Note on Torsion Points on Ample Divisors on Abelian Varieties

Hoshi, Yuichiro Research Institute for Mathematical Sciences, Kyoto University
Publication Date
2022-01
Abstract
In the present paper, we consider torsion points on ample divisors on abelian varieties. We prove that, for each integer n ≤ 2, an effective divisor of level n on an abelian variety does not contain the subgroup of n-torsion points. Moreover, we also discuss an application of this result to the study of the p-rank of cyclic coverings of curves in positive characteristic.
Keywords
abelian variety
torsion point
curve
p-rank
Comments
Mathematics Subject Classification. Primary 14K12; Secondary 14H30.