The topic for this semester is Faltings's proof of the Mordell conjecture.

- Organizers
- David Hansen and Daniel Gulotta
- Location and time
- Thursdays at 10:10AM in 622 Math

- [B] Binda, The Hodge-Tate decomposition theorem for Abelian Varieties over p-adic fields (following J.M. Fontaine)
- [BLR] Bosch, Lütkebohmert, Raynaud, Neron Models
- [CS] Cornell and Silverman, Arithmetic Geometry
- [D] Deligne, Preuve des conjectures de Tate et de Shafarevitch
- [dJ] Étale funamental groups (notes taken by Pak-Hin Lee for a course by Johan de Jong)
- [F] Fontaine, Formes différentielles et modules de Tate des variétés abéliennes sur les corps locaux
- [H] Seminar on Mordell Conjecture (notes taken by Jason Bland for 2012 Harvard seminar)
- [M] Faltings’s Proof of the Mordell Conjecture (notes taken by Takumi Murayama for 2016 Michigan seminar)
- [S] Stanford seminar
- [T1] Tate, Endomorphisms of abelian varieties over finite fields
- [T2] Tate, p-divisible groups
- Harvard seminar: 2012 2016

Date | Speaker | Topic | References |
---|---|---|---|

Jan 19 | Dan Gulotta | Special talk: Locally analytic distributions and the spectral halo | Preprint |

Jan 26 | David Hansen | Overview | [CS] 1-2, [T1] |

Feb 2 | Carl Lian | Abelian varieties | [S] 2 |

Feb 9 | Dmitrii Pirozhkov | Endomorphisms of abelian varieties over finite fields | [T1] |

Feb 16 | Shizhang Li | Néron models and reduction theorems | [BLR] 1, [H] 4, [dJ] |

Feb 23 | Qixiao Ma | Theory of heights | [CS] 6, [D] 1, [M] 3-4, [H] 5 |

Mar 2 | Dan Gulotta | Hodge-Tate decomposition for abelian varieties | [M] 5, [F], [B], [T2] |

Mar 9 | Sam Mundy | p-divisible groups | [M] 6, [T2], [CS] 3.3-3.6, [S] 4-5, 9 |

Mar 23 | Jingwei Xiao | p-divisible groups | [M] 6, [T2], [CS] 3.5-3.7, [S] 9-10 |

Mar 30 | Qixiao Ma | Behavior of Faltings height under isogeny | [M] 7, [S] 20 |

Apr 6 | Faltings isogeny theorem | [M] 8, [S] 20 | |

Apr 13 | Raynaud's theorem on finite flat group schemes | [M] 9 | |

Shafarevich and Mordell conjectures | [CS] 2.6, [S] 21-22 |

Possible additional topics: Siegel moduli schemes ([CS] 9, [H] 3), Arakelov intersection theory ([CS] 12), Hodge-Tate representations ([H] 9, [B])