Lectures on the Mordell-Weil Theorem [Paperback]

The book is based on a course given by J.-P. Serre at the Coll?ge de France in 1980 and 1981. Basic techniques in Diophantine geometry are covered, such as heights, the Mordell-Weil theorem, Siegel's and Baker's theorems, Hilbert's irreducibility theorem, and the large sieve. Included are applications to, for example, Mordell's conjecture, the construction of Galois extensions, and the classical class number 1 problem. Comprehensive bibliographical references.Contents: Heights - Nomalized heights - The Mordell-Weil theorem - Mordell's conjecture - Local calculation of normalized heights - Siegel's method - Baker's method - Hilbert's irreducibility theorem - Construction of Galois extensions - Construction of elliptic curves of large rank - The large sieve - Applications of the large sieve to thin sets.Professor Jean-Pierre Serre ist ein renommierter franz?sischer Mathematiker am Coll?ge de France, Paris.Neuauflage eines KlassikersSpringer Book Archives