Essential dimension of sequences of quadratic Pfister forms

Abstract

We study the essential dimension of the set of isometry classes of $m$-tuples $(\ddot{I}{†}_1,...,\ddot{I}{†}_m)$ of quadratic $n$-fold Pfister forms over a field $F$ such that the Witt class of $\ddot{I}{†}_1\perp \dots \perp \ddot{I}{†}_m$ lies in $I_q^{n+1}F$. We show that the essential dimension is equal to $n+1$, when $m=3$, and is either $4$ or $5$, when $n=\text{char}F=2$, $m=4$.