Essential dimension of sequences of quadratic Pfister forms

TL;DR

This paper investigates the minimal number of parameters needed to describe certain classes of quadratic Pfister forms over a field, revealing exact essential dimension values in specific cases.

Contribution

It determines the essential dimension of isometry classes of sequences of quadratic Pfister forms, providing new exact values for particular cases.

Findings

Essential dimension equals n+1 for m=3.

Essential dimension is 4 or 5 when n=char F=2 and m=4.

Provides explicit essential dimension values for specific Pfister form configurations.

Abstract

We study the essential dimension of the set of isometry classes of $m$-tuples $(\varphi_1,...,\varphi_m)$ of quadratic $n$-fold Pfister forms over a field $F$ such that the Witt class of $\varphi_1 \perp \ldots \perp \varphi_m$ 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 $n=\text{char} F=2$, $m=4$.