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The rank of abelian varieties over large algebraic fields

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Abstract.

Improving a theorem of Frey-Jarden from 1974 we prove for an infinite finitely generated field K and an Abelian variety A over K that rank \((A(K_{s} [{\varvec{\upsigma}}])) = \infty \) for almost all \({\varvec{\upsigma }} \in {\text{Gal}}(K)^{e} .\)

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Authors and Affiliations

  1. Mathematisches Institut, Erlangen University, Bismarckstr. 1 1/2, D-91054, Erlangen, Germany

    Wulf-Dieter Geyer

  2. School of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Moshe Jarden

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  1. Wulf-Dieter Geyer
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  2. Moshe Jarden
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Correspondence to Wulf-Dieter Geyer.

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Received: 7 March 2005

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Geyer, WD., Jarden, M. The rank of abelian varieties over large algebraic fields. Arch. Math. 86, 211–216 (2006). https://doi.org/10.1007/s00013-005-1492-x

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  • DOI: https://doi.org/10.1007/s00013-005-1492-x

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