Welcome to the Fall 2017 page for the Boston University Number Theory Expository Seminar!

Our topic this semester is Abelian Varieties. We will meet weekly and take turns giving lectures on various topics.

Our primary reference is the set of notes by Milne: Abelian Varieties

For the final 3 lectures we will be exploring the *Honda-Tate Theorem*. The reference we will be following is Edixhoven, Moonen, van der Geer (linked below).

Some other references of note:

- Edixhoven, Moonen, van der Geer, Abelian Varieties
- Mumford, "Abelian Varieties"
- Murty, "Introduction to Abelian Varieties"
- Notes by Cais, Abelian Varieties
- Polishchuk, "Abelian Varieties, Theta Functions and the Fourier Transform"
- Oort, Abelian Varieties over Finite Fields

**Time**: Friday 9am - 11am

**Location**: MCS 148

Week | Topic (Section in Milne) | Speaker | Notes |

1 (9/4-9/8) | Introduction/Overview, Background/Motivation (§ 1) | Angus | Lecture 1 |

2 (9/11-9/15) | Complex Theory (§ 2) | Alex | Lecture 2 |

3 (9/18-9/22) | Rational maps into AV, Cohomology (§ 3,4) | Maria | Lecture 3 |

4 (9/25-9/29) | Thm of the Cube (§ 5) | Ricky | Lecture 4 |

5 (10/2-10/6) | AV's are projective, Isogenies (§ 6,7) | Sachi | Lecture 5 |

6 (10/9-10/13) | The dual AV, the dual exact sequence (§ 8,9) | Angus | Lecture 6 |

7 (10/16-10/20) | Endomorphisms (§ 10) | Berke | Lecture 7 |

8 (10/23-10/27) | Polarizations, Étale Cohomology (§ 11,12) | Alex | Lecture 8 |

9 (10/30-11/3) | Weil Pairings (§ 13) | Maria | Lecture 9 |

10 (11/6-11/10) | Rosati Involution (§ 14) | Alex | Lecture 10 |

11 (11/13-11/17) | AVs over Finite Fields (§ 16.1,16.2 [Edix-vdG-Moon]) | Ricky | Lecture 11 |

12 (11/20-11/24) | NO MEETING (Thanksgiving) | ||

13 (11/27-12/1) | Tate's Theorem (§ 16.3,16.4 [Edix-vdG-Moon]) | Sachi | Lecture 12 |

14 (12/4-12/8) | Honda-Tate Thm (§ 16.5,16.6 [Edix-vdG-Moon]) | Angus | Lecture 13 |