Equivariant Bloch-Kato conjecture and non-abelian Iwasawa Main Conjecture

TL;DR

This paper explores the connection between the equivariant Bloch-Kato conjecture and the non-abelian Iwasawa Main Conjecture, discussing implications for special values of L-functions and the role of twisting in non-abelian cases.

Contribution

It clarifies the relationship between these conjectures and proposes a reduction approach for the non-abelian Main Conjecture using twisting techniques.

Findings

Relation established between Bloch-Kato and Iwasawa conjectures

Discussion of Dirichlet characters in the abelian case

Proposal to reduce non-abelian conjecture via twisting

Abstract

This is a contribution to the ICM 2002. We explain the relation between the (equivariant) Bloch-Kato conjecture for special values of L-functions and the Main Conjecture of (non-abelian) Iwasawa theory. On the way we will discuss briefly the case of Dirichlet characters in the abelian case. We will also discuss how "twisting" in the non-abelian case would allow to reduce the general conjecture to the case of number fields. This is one the main motivations for a non-abelian Main Conjecture.