On the work of Ritter and Weiss in Comparison with Kakde's Approach

TL;DR

This paper compares two recent approaches by Ritter-Weiss and Kakde in proving the non-commutative Iwasawa main conjecture over totally real fields, highlighting their similarities and differences.

Contribution

It provides a comprehensive survey contrasting Ritter-Weiss and Kakde's methods for the non-commutative Iwasawa main conjecture proof.

Findings

Both approaches prove the conjecture assuming the vanishing of a μ-invariant.

The methods differ in their technical frameworks and proof strategies.

The survey clarifies the relationship between the two proofs.

Abstract

Almost simultaneously Ritter and Weiss arXiv:1004.2578 on the one hand and Kakde arXiv:1008.0142 on the other hand gave a proof of the non-commutative Iwasawa main conjecture over totally real fields for the Tate motive under the assumption that a certain $\mu$-invariant vanishes as has been conjectured also by Iwasawa. In this notes we compare both approaches in a survey.