Hasse principle for G-trace forms

TL;DR

This paper establishes a local-global principle for G-trace forms and self-dual normal bases in G-Galois algebras over global fields of characteristic not 2, advancing understanding of their algebraic structure.

Contribution

It proves a new local-global principle for the existence and isomorphism of G-trace forms and self-dual normal bases in G-Galois algebras over global fields.

Findings

Proves a local-global principle for G-trace forms.

Establishes criteria for the existence of self-dual normal bases.

Provides conditions for isomorphism of G-trace forms.

Abstract

Let k be a global field of characteristic not 2. We prove a local-global principle for the existence of self-dual normal bases, and more generally for the isomorphism of G-trace forms, of G-Galois algebras over k.