Common Slots of Bilinear and Quadratic Pfister Forms

Abstract

We show that over any field $F$ of $\mathrm{char}(F)=2$ and 2-rank $n$, there exist $2^n$ bilinear $n$-fold Pfister forms that have no slot in common. This answers a question of Becher's in the negative. We provide an analogous result also for quadratic Pfister forms.