Roots of unity and torsion points of abelian varieties

2015/07/03 by Lombardo, Davide
#11G10 #11J95 #14K15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1507.00951

Abstract

We answer a question raised by Hindry and Ratazzi concerning the intersection between cyclotomic extensions of a number field K and extensions of K generated by torsion points of an abelian variety over K. We prove that a weak version of the property (μ) they introduced holds for any abelian variety, while the same is not true for a slightly stronger version of the property they also considered.

Related

• Torsion points of abelian varieties in abelian extensions
• Torsion of abelian varieties, Weil classes and cyclotomic extensions
• Torsion of Abelian varieties over solvable extensions of number fields
• Torsion bounds for a fixed abelian variety and varying number field
• Torsion of rank-two A-motives values in odd characteristic cyclotomic towers