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

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.

13 pages

References in corpus (1)

• Modules over Iwasawa algebras

Cited by in corpus (9)

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• On the leading terms of Zeta isomorphisms and p-adic L-functions in non-commutative Iwasawa theory
• The main conjecture of Iwasawa theory for totally real fields
• Proof of the Main Conjecture of Noncommutative Iwasawa Theory for Totally Real Number Fields in Certain Cases
• On a noncommutative Iwasawa main conjecture for varieties over finite fields
• Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p
• Characteristic elements in noncommutative Iwasawa theory
• On a Noncommutative Iwasawa Main Conjecture for Function Fields
• On non-commutative twisting in etale and motivic cohomology