Mathematics 207B

Topics in Number Theory

Image of modular Galois representations.

Winter Quarter 2013

Haruzo HIDA

Meeting Time: Regularly Mondays and Wednesdays 12:00 noon to 1:50 pm in MS 5233 and some Fridays 12:00 noon to 12:50 pm in MS 5233 (Friday meetings will be announced in the class before the meeting day).

Lecture Starts on Monday January 7th in MS 5233

Office hours: From 3:00pm (M) at my office: MS6308.

Texts: Lecture notes will be posted. The introduction of the notes:
Notes (face page, pdf file, posted) Notes (pdf file, expanded to cover up to the middle part covering lectures for 5-6 weeks, posted); Reference (a list of references, posted)

Grading will be based on student presentation on some Fridays (or in the student participating seminar). No final exam is planned.

As reference books, we list
[LFE]:"Elementary Theory of L-functions and Eisenstein Series," LMSST 26, Cambridge University Press, Cambridge, 1993, Chapters 5, 7
[GME]:"Geometric Modular Forms and Elliptic Curves," (World Scientific) First (2000) or Second edition (2011), Chapters 1, 2 and 4
[ALR]: Serre's book: "Abelian l-Adic Representations and Elliptic Curves," any edition, for example, Research Notes in Mathematics 7, A K Peters, 1998

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

In addition to above four topics,

Good understanding of the material covered by Math 210 series (including commutative and non-commutative algebra theory) and algebraic number theory.