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