Fields with bounded Brauer $2$-torsion index

TL;DR

This paper establishes a bound relating the dimension of certain quadratic forms to central division algebras of exponent 2 over fields of characteristic not 2, using quadratic trace form computations.

Contribution

It introduces a new bound connecting anisotropic quadratic Pfister forms with central division algebras of exponent 2, expanding understanding of their structural relationships.

Findings

Bound on the dimension of anisotropic quadratic Pfister forms

Relation between quadratic forms and central division algebras of exponent 2

Use of quadratic trace forms in proofs

Abstract

It is shown that, over a field of characteristic not $2$, the dimension of an anisotropic quadratic Pfister form of trivial total signature is at most twice the dimension of some central division algebra of exponent $2$. The proof is based on computations with quadratic trace forms of central simple algebras.