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 10.00-12.00, 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 p-adic fields.

  • Structure theory of Zp[[T]]-modules.

  • Iwasawa's control theory on Zp-extensions.

  • p-adic measures and the p-adic 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 p-adic fields.

Lecture 2 (October 19th). Structure theory of Zp[[T]]-modules.

Lecture 3 (October 26th). Iwasawa's control theory on Zp-extensions I.

Lecture 4 (November 2nd). Iwasawa's control theory on Zp-extensions II.

Lecture 5 (November 9th). p-adic measures and the p-adic 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.