Iwasawa Theory: A Climb up the Tower

Introduction to Iwasawa Theory

Iwasawa theory and generalizations

This is an introduction to Iwasawa theory and its generalizations. We discuss some main conjectures and related subjects. Mathematics Subject Classification (2000). Primary 11R23; Secondary 11G40, 14G10.

Iwasawa Theory for Elliptic Curves

The topics that we will discuss have their origin in Mazur’s synthesis of the theory of elliptic curves and Iwasawa’s theory of ZZp-extensions in the early 1970s. We first recall some results from Iwasawa’s theory. Suppose that F is a finite extension of Q and that F∞ is a Galois extension of F such that Gal(F∞/F ) ∼= ZZp, the additive group of p-adic integers, where p is any prime. Equivalentl...

Opening up the Ivory Tower

Big pharma is increasingly looking to academia for new drug leads and technologies; meanwhile universities are being forced to look beyond the National Institutes of Health (NIH) for funding. This mutual attraction-out-of-necessity is helping to forge new bonds between industry and academia.

On the Μ-invariant in Iwasawa Theory

The aim of this expository article is to discuss the μ-invariant associated to finitely generated modules over Iwasawa algebras. This is an important invariant which was first discovered by Iwasawa in the 1960’s and occurs in his seminal work on cyclotomic fields [9], [10]. In fact, Iwasawa conjectured that his μ-invariant was always zero for the pprimary subgroup of the ideal class group of th...