On the relative K-group in the ETNC, Part III

TL;DR

This paper extends previous work on the ETNC to include non-regular orders, especially integral group rings, by developing new methods applicable to non-commutative Gorenstein orders.

Contribution

It generalizes the main results of the ETNC to arbitrary non-commutative Gorenstein orders, including integral group rings, by modifying the module category used.

Findings

Successfully extended ETNC results to non-regular orders

Included integral group rings as a special case

Developed a new subcategory of modules for the theory

Abstract

The previous papers in this series were restricted to regular orders. In particular, we could not handle integral group rings, one of the most interesting cases of the ETNC. We resolve this issue. We obtain versions of our main results valid for arbitrary non-commutative Gorenstein orders. This encompasses the case of group rings. The only change we make is using a smaller subcategory inside all locally compact modules.