Lectures on the Mordell-Weil theorem

Inhaltsverzeichnis1. Summary.2. Heights.3. Normalised heights.4. The Mordell-Weil theorem.5. Mordell’s conjecture.6. Local calculation of normalised heights.7. Siegel’s method.8. Baker’s method.9. Hilbert’s irreducibility theorem.10. Construction of Galois extensions.11. Construction of elliptic curves of large rank.12. The large sieve.13. Applications of the large sieve to thin sets.Appendix: The class number 1 problem and integral points on modular curves.