Math 207c, 2011 Spring

Mathematics 207C
Topics in Number Theory

Galois Deformation, Modular Lifting and R=T Theorems

Spring Quarter 2011

Haruzo HIDA

Meeting Time: Mondays and Wednesdays 1:00pm to 2:50pm at MS 5217
Office hours: After class meetings, from 3:00pm (MW) at my office: MS6308.

Texts: Lecture notes will be posted: The first set of lecture notes:
Entire Notes (pdf file).

Grading will be based on student presentation (and possibly homework exercises in the lecture notes, perhaps, due mid-May). No final exam is planned. D

As reference books, we list
"Modular forms and Galois cohomology" (Cambridge studies in advanced mathematics 69)
"Geometric Modular Forms and Elliptic Curves" (World Scientific)

Topics: I would touch the following topics in this course:

Basics of Galois deformation theory (and representation theory of pro-finite groups);
Sketch of proofs of different R=T theorems.

Related topics will be touched upon in Math 290B student seminar on Mondays at 4:30pm-5:50pm in MS 5148 and Wednesdays at 3:30pm-4:50pm in MS 5127 (students are encouraged to attend).

Prerequisite:
Good understanding of commutative and non-commutative algebra, algebraic number theory, basic arithmetic geometry (old course notes on arithmetic modular forms/elliptic curves [pdf]) and basic Galois cohomology (old course notes on Galois cohomology [pdf]).