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Linkage of quadratic Pfister forms

ABSTRACT We study the necessary conditions for sets of quadratic n-fold Pfister forms to have a common (n−1)-fold Pfister factor. For any set S of n-fold Pfister forms generating a subgroup of of order 2s in which every element has an n-fold Pfister representative, we associate an invariant in which lives inside when the forms in S have a common (n−1)-fold Pfister factor. We study the properties of this invariant and compute it explicitly in a few interesting cases.