On the Nonexcellence of Field Extensions $F(\pi)/F$

For any $n\ge3$, we construct a field $F$ and an $n$-fold Pfister form $\varphi$ such that the field extension $F(\varphi)/F$ is not excellent. We prove that $F(\varphi)/F$ is universally excellent if and only if $\varphi$ is a Pfister neighbor of dimension $\le4$.

Keywords and Phrases: Quadratic forms, Pfister forms, excellent field extensions.

1991 Mathematics Subject Classification: Primary 11E04; Secondary 11E81, 12F20.

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