Comparing direct limit and inverse limit of even $K$-groups in non-commutative $p$-adic Lie extensions

TL;DR

This paper extends a duality between direct and inverse limits of higher even K-groups from commutative to certain non-commutative p-adic Lie extensions, advancing understanding in algebraic K-theory and number theory.

Contribution

It establishes a duality for higher even K-groups over non-commutative p-adic Lie extensions, generalizing previous results from commutative cases.

Findings

Duality established for non-commutative p-adic Lie extensions

Extends previous commutative case results

Advances understanding of K-theory in non-commutative Iwasawa theory

Abstract

In a previous paper of the author, we establish a duality for the direct limit and the inverse limit of higher even $K$-groups over a $\mathbb{Z}_p^d$-extension. In this paper, we shall establish such a duality over certain non-commutative $p$-adic Lie extensions.