The Multinorm Principle For Linearly Disjoint Galois Extensions

TL;DR

This paper proves a local-global principle for the multinorm problem in number theory, specifically for linearly disjoint Galois extensions, advancing understanding of norm behavior in algebraic extensions.

Contribution

It establishes a multinorm principle for linearly disjoint Galois extensions of global fields, extending previous results in algebraic number theory.

Findings

Proves the multinorm principle under linear disjointness conditions

Provides criteria for local-global norm equivalence in Galois extensions

Enhances understanding of norm behavior in algebraic extensions

Abstract

Let L_1 and L_2 be finite separable extensions of a global field K, and let E_i be the Galois closure of L_i over K for i=1,2. We establish a local-global principle for the product of norms from L_1 and L_2 (so-called multinorm principle) provided that the extensions E_1 and E_2 are linearly disjoint over K.