On universal norms and the first layers of Z_p-extensions of a number field

TL;DR

This paper characterizes the Kummer radical of the first layers of all Z_p-extensions of a number field containing a primitive p-th root of unity, using universal norms of p-units in the cyclotomic tower.

Contribution

It provides a new description of the Kummer radical in terms of universal norms, extending understanding of Z_p-extensions of number fields.

Findings

Kummer radical expressed via universal norms of p-units

Analysis of twisted radicals related to AF

Enhanced understanding of Z_p-extensions structure

Abstract

For an odd prime p and a number field F containing a primitive p-th root of unity, we describe the Kummer radical A_F of the first layers of all the Z_p-extensions of F in terms of universal norms of p-units along the cyclotomic tower of F . We also study "twisted" radicals related to AF .