Iwasawa theory and the Eisenstein ideal

Eisenstein Hecke Algebras and Conjectures in Iwasawa Theory

We formulate a weak Gorenstein property for the Eisenstein component of the p-adic Hecke algebra associated to modular forms. We show that this weak Gorenstein property holds if and only if a weak form of Sharifi’s conjecture and a weak form of Greenberg’s conjecture hold.

Selmer Groups and the Eisenstein-klingen Ideal

0 Introduction The central point in the Bloch-Kato conjectures is to establish formulas for the order of the Selmer groups attached to Galois representations in terms of the special values of their L-functions. In order to give upper bound, the main way is to construct Euler systems following Kolyvagin. Besides, lower bounds have been obtained by using congruences between automorphic forms. So,...

The Rank of Mazur’s Eisenstein Ideal

We use pseudodeformation theory to study Mazur’s Eisenstein ideal. Given prime numbers N and p > 3, we study the Eisenstein part of the p-adic Hecke algebra for Γ0(N). We compute the rank of this Hecke algebra in terms of Massey products in Galois cohomology, answering a question of Mazur and generalizing a result of Calegari-Emerton. We also also give new proofs of Merel’s result on this rank ...

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.

Introduction to Iwasawa Theory