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Clay Institute Summer School
The arithmetic of curves
From July 24 to August 4 I will be running a 15-hour mini-course on the
arithmetic of curves.
This mini-course is part of the
Clay Institute Summer School
that is taking place
in Gottingen, Germany, from July 17 to August 11, 2006.
The mini-course will be given in two parts, in two consecutive weeks,
and the syllabus is
roughly as follows.
Week 1: The key finiteness theorems (8 hours)
1. Overview
2. The Mordell-Weil theorem
3. Faltings' Theorem
4. Modular curves and Mazur's Theorem
5. Fermat curves and Wiles' Theorem
Week 2: Rational points on elliptic curves (7 hours)
1. Heegner points
2. The theorems of Gross-Zagier and Kolyvagin
3. Shimura curve parametrisations
4. p-adic uniformisation
5. Stark-Heegner points