Higher codimension behavior in equivariant Iwasawa theory for CM-fields

TL;DR

This paper advances the understanding of higher codimension behavior in equivariant Iwasawa theory for CM-fields by developing a new algebraic framework that extends previous results and offers refined insights.

Contribution

It introduces a general algebraic theory on perfect complexes, extending prior work to equivariant and non-equivariant settings for unramified Iwasawa modules.

Findings

Extended results to equivariant settings.

Provided refined analysis of higher codimension behavior.

Developed a new algebraic perspective on perfect complexes.

Abstract

In classical Iwasawa theory, we mainly study codimension one behavior of arithmetic modules. Relatively recently, F. M. Bleher, T. Chinburg, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi, and M. J. Taylor started studying higher codimension behavior of unramified Iwasawa modules which are conjectured to be pseudo-null. In this paper, by developing a general algebraic theory on perfect complexes, we obtain a new perspective of their work. That allows us to extend the results to equivariant settings and, even in non-equivariant settings, to obtain more refined results concerning the higher codimension behavior.