Iwasawa theory resources

Iwasawa theory is a branch of number theory with important applications to class groups of number fields and to conjectures on special values of zeta functions. Here are some starting points for learning more about this.

(You might find other references at Wikipedia and in this general MathOverflow question.)

Book references:

• Lang: Cyclotomic fields I and II (Google Books)
• Washington: Introduction to cyclotomic fields (Google Books)
• Neukirch, Schmidt, Wingberg: Cohomology of number fields (Google Books)
• Coates and Sujatha: Cyclotomic fields and zeta values
• Iwasawa Collected Papers (2 volumes)
• Noncommutative Iwasawa Main Conjecture over Totally Real Fields (SpringerLink)

Surveys and introductions online:

Manfred Kolster: K-theory and arithmetic (Very nice basic introduction to zeta values and Iwasawa theory)

The Kato ICM talk 2006

Introductory notes by Jim L. Brown

Surveys of Sujatha:

• The Main Conjecture (with Coates)
• On the mu-invariant

Surveys of Venjakob:

• From the BSD over the ETNC to noncommutative Iwasawa theory
• From classical to noncommutative Iwasawa theory

A survey of Greenberg. Other surveys, and a book draft, on Greenberg’s webpage.

Matthias Flach surveys:

• The equivariant Tamagawa number conjecture: A survey
• Iwasawa theory and motivic L-functions

A survey by Mitchell from the Handbook of K-theory, on Iwasawa theory and homotopy theory. (See also an interesting blog post of Eric Peterson here, for some possible connections with chromatic homotopy theory)

For noncommutative Iwasawa theory, here are some additional key papers:

• Fukaya and Kato: A formulation of conjectures on p-adic zeta functions in noncommutative Iwasawa theory
• The five-author paper
• Kakde: The main conjecture of Iwasawa theory for totally real fields from arXiv Front: math.KT by Mahesh Kakde. Some of this is reviewed in arxiv preprints by Venjakob and/or Schneider.
• Skinner and Urban: The Iwasawa main conjecture for GL2
• Various papers of David Burns
• The Bertolini-Darmon paper in Annals
• Malte Witte: Noncommutative Main Conjecture of Geometric Iwasawa Theory

Finally, a list of all papers on MathSciNet labelled with subject code 11R23 (Iwasawa theory), the latest papers on arXiv, and a MathOverflow search on “Iwasawa”.