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