Lectures on the Mordell-Weil Theorem

Inhaltsverzeichnis

• 1. 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.