On the kernel of the norm in some unramified number fields extensions

TL;DR

This paper investigates the structure of units in certain unramified number field extensions by computing the -1 Tate cohomology group, providing new insights into algebraic number theory.

Contribution

It explicitly determines the -1 Tate cohomology group of units for principal abelian extensions of type (p^a, p^b), a novel calculation in the field.

Findings

Computed the -1 Tate cohomology group for specific unramified extensions

Provided explicit descriptions of units in these extensions

Enhanced understanding of cohomological properties of number fields

Abstract

We determine the -1 Tate cohomology group of the units for principal abelian extensions of type (p^a, p^b) of a number field.