BUNTES: Complex Multiplication
2020 Fall
Fall 2020 BUNTES will cover the topic
of Complex Multiplication of Abelian Varieties. Due to
the world being on lock-down, all meetings will take place
on Zoom. Furthermore, instead of the usual format of having
2 hour talks, the ''speaker'' will instead function as an informed
discussion leader who will have read up on the designated topic
beforehand and prepared a short 15 to 30 min talk followed by
discussion topics.
The first half of the semester will be focused on complex
multiplication of elliptic curves with a focus on explicit
class field theory and galois representations. We will then
transition to the higher dimensional case of abelian varieties.
The main references will be Silverman's Advanced Topics in the
Arithmetic of Elliptic Curves [Silv]
for the first half and Milne's notes on Complex Multiplication
[MilneCM] for
the latter half. We will also be using
[MilneAV],
[Rubin],
and
[SilvI].
Meeting Times: Wednesday, 11:30 AM Eastern Time.
Zoom Meeting Code: 950 8454 3095
Password: cmbuntes
| Date | Topic | Speaker | Reference |
|---|---|---|---|
| 9/9 | Intro and Overview of CM | John Sim | Silverman |
| 9/16 | Elliptic Curves CM | Oana | Silv, II.1,.2 |
| 9/23 | Class Field Theory and j-inv | Ricky | Silv, II.3-7 |
| 9/30 | Grossencharacters and L-series | Angus | Silv, II.3-9 |
| 10/7 | L-series of Elliptic Curves | Jacksyn | SilvI, Appendix C.16 |
| 10/14 | Coates-Wiles CM BSD | John | Rubin, Ch. 10 |
| 10/21 | Intro to Abelian Varieties | Aash | MilneAV, I |
| 10/28 | Abelian Varieties with CM | Alex | MilneCM, I.3, II.7 |
| 11/4 | TBD | TBD | TBD |
| 11/11 | TBD | TBD | TBD |
| 11/18 | TBD | TBD | TBD |
| 11/25 | No meeting - Thanksgiving Break | N/A | Food |
| 12/2 | TBD | TBD | TBD |
| 12/9 | TBD | TBD | TBD |