BUNTES: Complex Multiplication

2020 Fall

Overview

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].

Announcements

Meeting Times: Wednesday, 11:30 AM Eastern Time.

Zoom Meeting Code: 950 8454 3095
Password: cmbuntes

Schedule

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