The Mordell-Weil Theorem
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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.
KeywordsAbelian Variety Number Field Finite Type Constant Field Abelian Extension
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© Springer Science+Business Media New York 1983