This is a website for the fall 2013 reading course on topological automorphic forms and abelian varieties. We're aiming to plunge about halfway through Behrens and Lawson's manuscript.

- On
**October 3**, Paul VanKoughnett talked about*p*-divisible groups. - On
**October 10**, Johan Konter introduced abelian varieties and sketched the Honda-Tate theorem classifying abelian varieties over finite fields up to isogeny. - On
**October 17**, Johan Konter classified abelian varieties over the algebraic closure of a finite field. - On
**October 24**, Joel Specter gave some examples of abelian varieties over**C**. - On
**October 25**, Joel Specter talked about the relationship between abelian varieties in characteristic 0 and abelian varieties over finite fields, and gave an example involving counting points on a Fermat curve. - On
**October 31**, Philip Egger talked about level structures. - On
**November 5**, Dylan Wilson talked about Lurie's realization theorem and defined Deligne-Mumford stacks. - On
**November 7**, Dylan Wilson continued to discuss Lurie's theorem. - On
**November 12**, Rob Legg defined polarizations and complex multiplication. - On
**November 14**, Paul VanKoughnett constructed the Shimura varieties used by Behrens and Lawson. - On
**November 19**, Paul VanKoughnett constructed TAF.

References and other resources:

**General:**Doug Ravenel's TAF seminar. Tyler Lawson's survey paper.**Chromatic homotopy theory background:**The Northwestern pre-Talbot seminar. The 2013 Talbot workshop. Jacob Lurie's course notes. Mike Hopkins' course notes.**p-divisible groups**: Demazure's monograph. (All the stuff on this website might be worth a look.) Messing's book (more general and more schemey than Demazure). Tate's paper. A course by Ren\'e Schoof on finite group schemes.**Abelian varieties**: Mumford's book*Abelian Varieties*is the canonical reference. Milne's course notes. The Honda-Tate classification; notes by Kirsten Eisenträger and Frans Oort.**Level structures**: The canonical reference (for elliptic curves, at least, though the general situation isn't really harder) is the first few chapters of Katz-Mazur, which doesn't seem to be available online.**Lurie's theorem**doesn't have a published proof, but statements and discussions of it can be found in chapter 7 of Behrens-Lawson, and in Goerss's TMF notes.**Stacks**: If you can read French, Laumon—Moret-Bailly might be worth looking at. If you can read encyclopedias, there's always the Stacks project. Anton Geraschenko has some notes for a course by Martin Olsson. My favorite reference, for the homotopically minded, is Goerss's notes on the moduli stack of formal groups, which teaches a lot about stacks through a single example that's central to chromatic homotopy theory.**Shimura varieties**: Behrens-Lawson's main references are*The Geometry and Cohomology of Some Simple Shimura Varieties*by Harris and Taylor;*p-Adic Automorphic Forms on Shimura Varieties*by Hida; and "Points on some Shimura Varieties over Finite Fields" by Kottwitz (the most accessible, which isn't saying much).**The Serre-Tate theorem**: This article by Katz is the best source. Akhil Mathew has a good discussion on his blog.