Roots of unity and torsion points of abelian varieties

Davide Lombardo

Roots of unity and torsion points of abelian varieties

Algebraic Geometry 2016-01-01 v3

Authors: Davide Lombardo

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 $(\mu)$ they introduced holds for any abelian variety, while the same is not true for a slightly stronger version of the property they also considered.

Keywords

roots of unity torsion points abelian varieties cyclotomic extensions number fields property (mu)

Cite

@article{arxiv.1507.00951,
  title  = {Roots of unity and torsion points of abelian varieties},
  author = {Davide Lombardo},
  journal= {arXiv preprint arXiv:1507.00951},
  year   = {2016}
}

Comments

18 pages. v3: the result is now independent of the truth of the Mumford-Tate conjecture

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