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


Eisenstein congruences and Selmer groups


Eric Urban

Columbia University


Abstract

There is an intimate relation between Selmer groups and congruences between Eisenstein series and cusp forms. This fact has been illustrated in the proof of some Iwasawa-Greenberg Main Conjectures by constructing lower bounds for the size of Selmer groups. The purpose of this talk is to go over some examples of this relation as well as to explore some of its new aspects and related open questions.