Iwasawa theory of totally real fields for certain non-commutative $p$-extensions

TL;DR

This paper proves the Iwasawa main conjecture for totally real fields within specific non-commutative $p$-adic Lie extensions, extending previous results using integral logarithms.

Contribution

It generalizes Kato's proof of the main conjecture to certain non-commutative $p$-extensions of totally real fields.

Findings

Proves the Iwasawa main conjecture in new non-commutative settings

Utilizes integral logarithms by Oliver and Taylor

Extends Kato's results to Heisenberg type extensions

Abstract

In this paper, we prove the Iwasawa main conjecture of totally real fields for certain specific non-commutative $p$-adic Lie extensions, using the integral logarithms introduced by Oliver and Taylor. Our result gives certain generalization of Kazuya Kato's proof of the main conjecture for Galois extensions of Heisenberg type.