D\'emonstration g\'eom\'etrique du th\'eor\`eme de Lang-N\'eron
Abstract
We give a proof without heights of the Lang-N\'eron theorem: if K/k is a regular extension of finite type and A is an abelian K-variety, the group A(K)/K/k A(k) is finitely generated, where 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\'eron-Severi groups.
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