We will meet Wednesdays 14:30-16:00 in MCS B21.

Contact Jacksyn Bakeberg (bakeberg"at"bu.edu) for more information.

The plan is to follow J. Milne's 2017 notes. Other references include:

- Pierre Deligne (1971) Travaux de Shimura. (French)
- Kai-Wen Lan (2016) An Example-Based Introduction to Shimura Varieties.
- Ana Caraiani (2017) Lecture Notes on Perfectoid Shimura Varieties (Section 2 only).
- Henri Darmon (2003) Rational Points on Modular Elliptic Curves, Chapter 4 (Shimura Curves).

- Alex Youcis (2015) Shimura Varieties: Motivation. (Blog post).
- James Milne (2012) What is a Shimura Variety?.

Week | Speaker | Material | Reference |
---|---|---|---|

Week 1 (Sept. 8) | Jacksyn | Overview and motivation. Review of modular curves. | Caraiani (2017) pp 1-4. |

Week 2 (Sept. 15) | John | Shimura curves. | Darmon (2003). |

Week 3 (Sept. 22) | Steve | Algebraic groups, manifolds, Hermitian symmetric domains. | Lan (2016) 2.1, 2.2, 3.1; Milne (2017) Ch. 1. |

Week 4 (Sept. 29) | Cong | Complex abelian varieties, Hodge structures. | Milne (2017) pp 71-73; ibid. Ch. 2; Caraiani (2017) pp 13-17. |

Week 5 (Oct. 6) | Aash | Variations of Hodge structures. | Caraiani (2017) pp 15-17; Milne (2017) pp 28-31. |

Week 6 (Oct. 13) | Aash / Jacksyn | Examples of variations. | Weinstein (2013). |

Week 7 (Oct. 20) | Steve | Shimura data and varieties. | Caraiani (2017) pp 17-21; Milne (2017) pp 52-58; Lan (2016) pp 9-12. |

Week 8 (Oct. 27) | Jacksyn | Examples: Elliptic, Hilbert, and Siegel modular varieties. | Milne (2017) pp 67-75; Cariani (2017) pp 19-21; Lan (2016) section 3. |

Week 9 (Nov. 3) | Jacksyn / Steve | Shimura varieties of Hodge type; PEL Shimura varieties; general Shimura varieties. | Milne (2017) ch 7-9; Weinstein (2013). |

Week 10 (Nov. 10) | John | CM: Shimura-Taniyama formula and the main theorem. | Milne (2017) ch 10-11. |

Week 11 (Nov. 17) | Cong | Definition of canonical models. | Milne (2017) ch 12. |

Week 12 (Nov. 24) | No meeting | Thanksgiving | |

Week 13 (Dec. 1) | Aash | Uniqueness and existence of canonical models. | Milne (2017) ch 13-14. |

Week 14 (Dec. 8) | Jacksyn | Examples and review. |

Last updated: 8 December 2021