SNOQIT I: Growth of $\Lambda$-modules and Kummer theory

TL;DR

This paper proves the Gross-Kuz'min conjecture for CM extensions of Q by analyzing the growth of Lambda modules related to ideal class groups, providing new insights into their structure and behavior.

Contribution

It introduces a novel approach to studying the growth of Lambda modules and proves the Gross-Kuz'min conjecture for a broad class of number fields.

Findings

Proof of the Gross-Kuz'min conjecture for CM extensions of Q.

Detailed analysis of the growth of Lambda modules at finite levels.

New results on the structure of p-parts of ideal class groups.

Abstract

The paper contains at the end a proof of the conjecture of Gross - Kuz'min, for CM extensions of Q. The main topic of the paper is the investigation of the growth of order and ranks at finite levels of some Lambda modules (p-parts of ideal class groups).