Topics in Number Theory
Winter Quarter 2014
Base Change and Galois Deformation
Meeting Time: Mondays and Wednesdays 1:00pm to
1:50pm, Fridays 4:00pm-5:50pm in MS 6201 (sometimes, we meet at 1pm on Fridays depending on schedule).
Office hours: After class meetings, from 4:00pm (MW)
at my office: MS6308.
Lecture Starts on Monday January 13th in MS 6201
Texts: Lecture notes will be posted: The first set of lecture
Grading will be based on student presentation at the end of courses on topics close to the course material).
No final exam is planned.
Notes (pdf file, a tentative version now posted).
As a reference book,
"Modular forms and Galois cohomology" (Cambridge studies in advanced mathematics 69).
Topics: I would touch the following topics in this course:
- Basics of Galois deformation theory (and representation theory of pro-finite groups);
- Relation of deformation rings for a given starting representation
restricted to open subgroups;
- Introduction to Galois cohomology;
- ``R=T" theorem, applications and open questions (if time allows).
- Related topics will be touched upon in Math 290B student seminar
on Wednesdays at 4:30pm-5:50pm and possibly
Mondays at 4:30pm-5:50pm both in MS 5117 (students are encouraged to attend).
Good understanding of commutative and non-commutative algebra,
algebraic number theory and very basics of Galois cohomology.