Number theory learning seminar 2010-2011

The topic for 2010-2011 is Faltings' proof of the Mordell conjecture. Familiarity with various basic topics in arithmetic geometry (schemes, class field theory, abelian varieties, etc.) is assumed whenever needed to get through a lecture in finite time.

Here are some references relevant to this year's seminar:
[N] Neron Models (Bosch, Lutkbohmert, Raynaud)
[C] Siegel moduli schemes and their compactifications (Chai) in "Arithmetic Geometry"
[D] Conjectures de Tate et Shafarevich (Deligne)
[L] Algebraic Geometry and Arithmetic Curves (Q. Liu)
[Mi] Abelian varieties (Milne) in "Arithmetic Geometry"
[Mu] Geometric Invariant Theory (Mumford)
[R] Schemas en groupes de type (p,...,p) (Raynaud)
[Sch] Introduction to finite group schemes (Schoof)
[Sh] Group schemes, formal groups, and p-divisible groups (Shatz) in "Arithmetic Geometry"
[S1] Advanced topics in the arithmetic of elliptic curves (Silverman)
[S2] Heights and elliptic curves (Silverman) in "Arithmetic Geometry"
[T1] p-divisible groups (Tate)
[T2] Finite flat group schemes (Tate) in "Modular Forms and Fermat's Last Theorem"

Notes -- use at your own risk.

These are informal notes. They may change without warning.

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 [Mu, App. I] .pdf
4, 5 Oct. 13, 20 Samit Introduction to finite flat group schemes ([T2], [Sch], [Sh]) .pdf
6 Oct. 7 Simon Cartier duality ([T2], [Sch], [Sh]) .pdf
7 Nov. 3 Melanie Raynaud's results on F-vector group schemes I [R] .pdf
8 Nov. 10 Rebecca Raynaud's results on F-vector group schemes II [R] .pdf
9 Nov. 17 Mike p-divisible groups I [T1, Ch. 2] .pdf
10 December Brandon p-divisible groups II ([R, section 1], [T1, Ch. 4]) .pdf
Winter quarter
11 January Sam Neron models ([N], [S], [Mu, Ch. 6]) .pdf
12 January Christian Semistable reduction I ([L], [N]) .pdf
13 February Brian Semistable reduction II ([N], SGA7) .pdf
14 February Brian Some finiteness theorems [Mi, section 18] .pdf
15 February Akshay Log singularities [D, p. 34]
16 February Brian Gabber's Lemma [D, pp. 32-34] .pdf
Spring quarter
17 March Payman No abelian varieties over Z [Sch]
18 March Peter Baily-Borel compactification .pdf
19 March Brandon Tate Conjecture .pdf
20 March Mike Faltings' finiteness theorem .pdf
21 April Rebecca Mordell conjecture .pdf