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"
Fall quarter | ||||
1 | Sept. 23 | Akshay | Overview and a toy model | |
2 | Sept. 29 | Brian | Introduction to abelian varieties | |
3 | Oct. 6 | Sam | Tate conjecture over finite fields [Mu, App. I] | |
4, 5 | Oct. 13, 20 | Samit | Introduction to finite flat group schemes ([T2], [Sch], [Sh]) | |
6 | Oct. 7 | Simon | Cartier duality ([T2], [Sch], [Sh]) | |
7 | Nov. 3 | Melanie | Raynaud's results on F-vector group schemes I [R] | |
8 | Nov. 10 | Rebecca | Raynaud's results on F-vector group schemes II [R] | |
9 | Nov. 17 | Mike | p-divisible groups I [T1, Ch. 2] | |
10 | December | Brandon | p-divisible groups II ([R, section 1], [T1, Ch. 4]) | |
Winter quarter | ||||
11 | January | Sam | Neron models ([N], [S], [Mu, Ch. 6]) | |
12 | January | Christian | Semistable reduction I ([L], [N]) | |
13 | February | Brian | Semistable reduction II ([N], SGA7) | |
14 | February | Brian | Some finiteness theorems [Mi, section 18] | |
15 | February | Akshay | Log singularities [D, p. 34] | |
16 | February | Brian | Gabber's Lemma [D, pp. 32-34] | |
Spring quarter | ||||
17 | March | Payman | No abelian varieties over Z [Sch] | |
18 | March | Peter | Baily-Borel compactification | |
19 | March | Brandon | Tate Conjecture | |
20 | March | Mike | Faltings' finiteness theorem | |
21 | April | Rebecca | Mordell conjecture |