Number theory learning seminar 2010-2011

The topic for 2010-2011 is Faltings' proof of the Mordell conjecture; in past years we covered modularity lifting (2009) and the proof of the Weil conjectures (2008).

Here's the schedule. The speaking slots are tentative, not set in stone: please do contact Brian or Akshay and express your keen desire to speak.

Notes -- use at your own risk.

These are informal notes written by each speaker. They may be riddled with errors. They may also change from time to time as we edit them. If you are a participant in the seminar, please contact Akshay to share the Dropbox folder where these notes are kep; this also allows to edit out typos from other peoples' notes.

Fall quarter
1 Sept 23 Akshay Overview and a toy model pdf
2 Sept 29 Brian Introduction to abelian varieties pdf
3 Oct 6 Sam Tate conjecture over finite fields pdf
4 Oct 13 Samit Introduction to finite flat group schemes See below.
5 Oct 20 Samit Introduction to finite flat group schemes, continued pdf
6 Oct 27 Simon Cartier duality pdf
7 Nov 3 Melanie Raynaud's results on F-vector group schemes. pdf
8 Nov 10 Rebecca Raynaud's results on F-vector group schemes. pdf
9 Nov 17 Mike p-divisible groups pdf
10 December Brandon p-divisible groups II pdf
Winter quarter
11 January Sam Neron models pdf
12 January Christian Semistable reduction, I pdf
13 February Brian Semistable reduction, II pdf
14 February Brian Some finiteness theorems pdf
15 February Akshay Log singularities
16 February Brian Gabber's lemma pdf
Spring quarter
17 March Payman Fontaine's proof that there are no abelian varieties over Z
19 March Peter Baily-Borel compactification pdf
20 March Brandon Tate Conjecture pdf
21 March Mike Faltings' finiteness theorem pdf
22 April Rebecca Mordell conjecture pdf