Ramification in Iwasawa Theory and Splitting Conjectures

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.

Galois modules, Iwasawa theory and leading term conjectures

Equivariant Iwasawa theory and non-abelian Starck-type conjectures

We discuss three di erent formulations of the equivariant Iwasawa main conjecture attached to an extension K/k of totally real elds with Galois group G, where k is a number eld and G is a p-adic Lie group of dimension 1 for an odd prime p. All these formulations are equivalent and hold if Iwasawa's μ-invariant vanishes. Under mild hypotheses, we use this to prove non-abelian generalizations of ...

The Iwasawa Main Conjectures for Gl2

1.1. The Iwasawa-Greenberg Main Conjecture. Let p be an odd prime. Let Q ⊂ C be the algebraic closure of Q in C. We fix an embedding Q ↪→ Qp. For simplicity we also fix an isomorphism Qp ∼= C compatible with the inclusion of Q into both. We let Q∞ be the cyclotomic Zp-extension of Q and ΓQ := Gal(Q∞/Q) its Galois group. The reciprocity map of class field theory identifies 1 + pZp with ΓQ; we le...

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.