Abstract
We consider abelian varieties, defined over essentially global fields, namely, those of §2, §3, §4, Chapter 2. We shall prove an absolute result and a relative one concerning the group of rational points of an abelian variety over such fields, namely:
Theorem 1. Let K be a finitely generated field over the prime field. Let A be an abelian variety defined over K. Then A(K) is finitely generated.
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© 1983 Springer Science+Business Media New York
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Lang, S. (1983). The Mordell-Weil Theorem. In: Fundamentals of Diophantine Geometry. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1810-2_6
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DOI: https://doi.org/10.1007/978-1-4757-1810-2_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2818-4
Online ISBN: 978-1-4757-1810-2
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