Math 849, A Proof of Fermat's Last Theorem - Spring 2018
Nigel Boston
Contact Information
303 Van Vleck Hall
Telephone: 263-4753.
E-mail: boston@math.wisc.edu
Homepage
Office Hours: TBA.
Sections
- Lecture: MWF 9:55-10:45, B235 VV.
Useful Web Materials
To Get a Grade
(1) Take notes for two classes and produce a careful clear TeX version
(2) Write a class project (10 to 20 pages) on one of the topics listed below or something of your own choice
(3) Give a 10 to 15 minute presentation to the class and to me on the same project
Suggested Topics
1. The abc conjecture.
2. Fermat-like equations.
3. Examples of Serre's conjecture and applications.
4. Families of elliptic curves with given mod p Galois representation.
5. More on Ribet's raising and lowering the level.
6. Group schemes and work of Khare et al.
7. More cases of the Fontaine-Mazur conjecture.
8. Kummer's work on regular primes.
9. Framed deformations.
10. Further properties of modular curves.
11. Profinite group theory.
12. Pseudo-representations.
13. The presentation of the absolute Galois group of the p-adics.
14. Explicit examples of modular curves.
15. Comparing the different constructions of universal deformation rings.
16. Fermat's last theorem over other rings (number rings, function fields, etc.).
17. Congruences of modular forms and Galois representations.
18. The modularity of mod 3 Galois representations.
19. Even Galois representations.
20. Brumer-Kramer proof of non-existence of elliptic curves of certain conductors.
21. Faltings-Serre method for finding all elliptic curves of small conductor.
22. Modular symbols and calculating with elliptic curves.
TeX Write-Ups of Sections
Schedule of Final Presentations
Some Final Projects