Open questions and recent developments in Iwasawa theory

Open questions and recent developments in Iwasawa theory
in honor of Ralph Greenberg's 60th birthday
June 2005


Iwasawa theory for Kummer extensions


Romyar Sharifi

McMaster University


Abstract

I will give a partially conjectural outline of relationships between several different objects: classical Iwasawa modules over Kummer extensions of cyclotomic fields, Greenberg's strict Selmer groups for reducible two-dimensional representations arising from Hida families of cusp forms congruent to Eisenstein series, cup products in Galois cohomology and reciprocity maps constructed from them, and two-variable p-adic L-functions of Mazur-Kitigawa/Greenberg-Stevens.