Abelian varieties over finitely generated fields and the conjecture of Geyer and Jarden on torsion

Details Abelian varieties over finitely generated fields and the conjecture of Geyer and Jarden on torsion Abelian varieties over finitely generated fields and the conjecture of Geyer and Jarden on torsion

2010-10-12

arxiv.org/abs/1010.2444v2

Mathematics

Algebraic Geometry

Second version of the manuscript

Scientific paper

In this paper we prove the Geyer-Jarden conjecture on the torsion part of the Mordell-Weil group for a large class of abelian varieties defined over finitely generated fields of arbitrary characteristic. The class consists of all abelian varieties with big monodromy, i.e., such that the image of Galois representation on l-torsion points, for almost all primes l, contains the full symplectic group.

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