The Mordell-Weil Theorem

Serge Lang
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Serge Lang: Yale University, Department of Mathematics

Chapter Chapter 6 in Fundamentals of Diophantine Geometry, 1983, pp 138-157 from Springer

Abstract: 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.

Keywords: Abelian Variety; Number Field; Finite Type; Constant Field; Abelian Extension (search for similar items in EconPapers)
Date: 1983
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DOI: 10.1007/978-1-4757-1810-2_6

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