On The Multinorm Principle For Finite Extensions

TL;DR

This paper investigates the multinorm principle for pairs of finite abelian extensions over global fields, providing explicit computations of the obstructions to this principle.

Contribution

It offers a precise calculation of the obstruction to the multinorm principle for finite abelian extensions, advancing understanding in algebraic number theory.

Findings

Computed the obstruction to the multinorm principle for specific pairs of extensions

Provided explicit formulas for the obstruction in the abelian case

Enhanced the theoretical framework for understanding multinorm principles

Abstract

Let L_1 and L_2 be finite abelian extensions of a global field K. We compute the obstruction to the multinorm principle for the pair L_1, L_2.