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

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.