The Mordell-Weil Theorem

  • Kenneth Ireland
  • Michael Rosen
Part of the Graduate Texts in Mathematics book series (GTM, volume 84)


In this chapter we prove the celebrated theorem of Mordell—Weil for elliptic curves defined over the field of rational numbers. Our treatment is elementary in the sense that no sophisticated results from algebraic geometry are assumed. It is our desire to present a self-contained treatment of this important result. The significance and implications of this theorem for contemporary research in diophantine geometry are farreaching. In the following chapter a summary without proofs of these developments to the present time is sketched. We hope that these two chapters will inspire the interested student to continue this study by consulting the more comprehensive texts on the arithmetic of elliptic curves listed in the bibliography to this chapter.


Modular Form Elliptic Curve Rational Point Elliptic Curf Abelian Variety 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Kenneth Ireland
  • Michael Rosen
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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