Meets: W 13.15-15.00 in von Neumann 1.023.
Starts: 15.4.2014.
The main goal of the semester is to understand some aspects of Faltings' proofs of some far--reaching finiteness theorems about abelian varieties over number fields, the highlight being the Tate conjecture, the Shafarevich conjecture, and the Mordell conjecture. There are a variety of references, including:
15.04.2015: Overview (Ben).
22.04.2015: Abelian varieties over arbitrary fields (Daniele). Notes.
29.04.2015: Tate module (Gregor). Notes.
06.05.2015: Tate and Shafarevich conjectures from finiteness (Niels). Notes.
13.05.2015: Group schemes (Eva).
20.05.2015: Heights (Daniele). Notes.
27.05.2015: Ramification of p-divisible groups (Antareep).
03.06.2015: Proof of the Tate conjecture (Wouter). Notes.
10.06.2015: Ramification of finite group schemes (Fabio).
17.06.2015: Finiteness of isogeny classes (Emre). Notes.
24.06.2015: Heights within isogeny classes and the Shafarevich conjecture (Barbara).
01.07.2015: The Mordell conjecture (Rostislav).