The Mordell-Weil Theorem

  • Serge Lang
Chapter

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 
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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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