A Mordell-Weil theorem for abelian varieties over fields generated by torsion points

2005/03/18 by Michael Larsen, Larsen, Michael · 1 citation
Computer Science · Mathematics · #11G10 #11R34 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11G10 #msc:11R34

paper · pdf · doi:10.48550/arxiv.math/0503378

8 pages

arxiv created 2005/03/18 · openalex publication_date 2005/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If A is an abelian variety over a number field K, and L is a (possibly infinite) extension of K generated by torsion points of A, then the quotient of A(L) by its torsion subgroup is a free abelian group.

Cited by

• Model theory of special subvarieties and Schanuel-type conjectures

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