On the nonexcellence of field extensions $F(\pi )/F$

Abstract

For any $n\ge 3$, we construct a field $F$ and an $n$-fold Pfister form $\phi$ such that the field extension $F(\phi )/F$ is not excellent. We prove that $F(\phi )/F$ is universally excellent if and only if $\phi$ is a Pfister neighbor of dimension $\le 4$.