IWASAWA THEORY (TCC COURSE)
This is the webpage for my TCC course on Iwasawa theory.
Main reference:
Cyclotomic Fields and Zeta Values (J. Coates and R. Sujatha).
Auxiliary references:
Introduction to Cyclotomic Fields (L. C. Washington).
Iwasawa theory (lecture notes of R. Sharifi, available at https://www.math.ucla.edu/~sharifi/iwasawa.pdf).
Lectures: Tuesday mornings 10.0012.00, from 12 Oct 2021 onwards.
Assessment of the course will be based on 3 problem sheets, to be distributed after lectures 2, 5 and 7.
Sheet 1 (review of algebraic number theory + structure theory of Zp[[T]] modules). Here (to be added). Deadline: November 9th.
Sheet 2. Here (to be added). Deadline: November 30th.
Sheet 3. Here (to be added). Deadline: December 24th.
Syllabus (to be added in detail).

The Iwasawa main conjecture: an overview.

Review of algebraic number theory and padic fields.

Structure theory of Zp[[T]]modules.

Iwasawa's control theory on Zpextensions.

padic measures and the padic zeta function.

Coleman power series.

The Iwasawa theorem.

TBD: either "A short introduction to Euler systems" or "A short introduction to Hida theory", discussing the relations with the Iwasawa main conjecture.
Tentative schedule
Lecture 1 (October 12th). Cyclotomic fields. Overview of Iwasawa theory. Brief review of padic fields.
Lecture 2 (October 19th). Structure theory of Zp[[T]]modules.
Lecture 3 (October 26th). Iwasawa's control theory on Zpextensions I.
Lecture 4 (November 2nd). Iwasawa's control theory on Zpextensions II.
Lecture 5 (November 9th). padic measures and the padic zeta function.
Lecture 6 (November 16th). Coleman power series.
Lecture 7 (November 23th). The Iwasawa theorem.
Lecture 8 (November 30th). Either "A short introduction to Euler systems" or "A short introduction to Hida theory", discussing the relations with the Iwasawa main conjecture.