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 |