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

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 Gal...

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Bibliographic Details
Published in:Mathematische Nachrichten 2013-09, Vol.286 (13), p.1269-1286
Main Authors: Arias-de-Reyna, Sara, Gajda, Wojciech, Petersen, Sebastian
Format: Article
Language:English
Subjects:
11G10
14K15
Abelian variety
Galois representation
Haar measure MSC 11E30
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Summary: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.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201200217