Mathematics 207a

Number Theory


Cyclicity in Iwasawa's theory

Winter Quarter 2018

Haruzo HIDA

Meeting Time: Mondays, Wednesdays and Fridays 2:00pm to 2:50pm in MS 6201.

Although this is a topic course, the content is elementary and good for first year students.
Here is a link to an overview of the course [pdf].
Office hours: Before the class meeting on Monday/Wednesday 1pm-1:50pm at my office: MS6308.

Lecture Starts on Monday January 8th at 2pm in MS 6201


Lecture notes:
Lecture notes now posted (pdf file, an expanded almost complete version of 1/9/18).

Grading will be based on student presentation either in the seminar course Math 290b.2.18w or in the class meeting at the end of courses on topics (close to the course material) chosen by each student. No final exam is planned.

As reference books, we suggest

  • [ICF] L. C. Washington, "Introduction to cyclotomic fields", Springer Graduate texts in Mathematics, (any edition),
  • [LFE] H. Hida, "Elementary Theory of L-functions and Eisenstein Series", LMSST 26, Cambridge University Press, Cambridge, 1993.
  • Topics: In this course, assuming basic knowledge of complex analysis, we describe basics of elliptic modular forms. We hope to cover the following four topics:

  • Class number formulas,
  • Basics of cyclotomic fields and Iwasawa theory,
  • Stickelberger's theorem,
  • Cyclicity over the Iwasawa algebra of the cyclotomic Iwasawa module.
  • Prerequisite:
    Good understanding of commutative algebra and algebraic number theory.