Démonstration géométrique du théorème de Lang-Néron

Details Démonstration géométrique du théorème de Lang-Néron Démonstration géométrique du théorème de Lang-Néron

2007-03-02

arxiv.org/abs/math/0703063v1

Motives and algebraic cycles: a celebration in honour of Spencer J. Bloch, Fields Institute Communications 56, AMS, 2009, 149-

Mathematics

Algebraic Geometry

Scientific paper

We give a proof without heights of the Lang-N\'{e}ron theorem: if $K/k$ is a
regular extension of finite type and $A$ is an abelian $K$-variety, the group
$A(K)/\Tr_{K/k} A(k)$ is finitely generated, where $\Tr_{K/k} A$ denotes the
$K/k$-trace of $A$ in the sense of Chow. Our method computes the rank of this
group in terms of certain ranks of N\'{e}ron-Severi groups.

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