Synopses & Reviews
The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives. Non-commutative Iwasawa theory has emerged dramatically over the last decade, culminating in the recent proof of the non-commutative main conjecture for the Tate motive over a totally real p-adic Lie extension of a number field, independently by Ritter and Weiss on the one hand, and Kakde on the other. The initial ideas for giving a precise formulation of the non-commutative main conjecture were discovered by Venjakob, and were then systematically developed
Synopsis
Preface.- John Coates, Dohyeong Kim: Introduction to the work of M. Kakde on the non-commutative main conjectures for totally real fields.- R. Sujatha: Reductions of the main conjecture.- Ted Chinburg, Georgios Pappas, Martin J. Taylor: The group logarithm past and present .- Peter Schneider, Otmar Venjakob: K_1 of certain Iwasawa algebras, after Kakde.- Mahesh Kakde: Congruences between abelian p-adic zeta functions.- Otmar Venjakob: On the work of Ritter and Weiss in comparison with Kakde's approach.- Malte Witte: Noncommutative Main Conjectures of Geometric Iwasawa Theory.
Table of Contents
Preface.- John Coates, Dohyeong Kim: Introduction to the work of M. Kakde on the non-commutative main conjectures for totally real fields.-