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

摘要

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 theMain Conjecture of (non-abelian) Iwasawa theory. On the way we will discussbriefly the case of Dirichlet characters in the abelian case. We will alsodiscuss how "twisting" in the non-abelian case would allow to reduce thegeneral conjecture to the case of number fields. This is one the mainmotivations for a non-abelian Main Conjecture.