Invariant for Sets of Pfister Forms

2024/03/29 by Chapman, Adam, Levin, Ilan · 1 citation
#11E81 #13A35 #16K20 20G10 #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #Primary 19D45 #Secondary 11E04

paper · doi:10.48550/arxiv.2404.00121

Abstract

We associate an (n₁+…+n_t-k(t-1))-fold Pfister form to any t-tuple of k-linked Pfister forms of dimensions 2^n₁,…,2^n_t, and prove its invariance under the different symbol presentations of the forms with a common k-fold sub-symbol. We then show that it vanishes when the forms are actually (k+1)-linked or when the characteristic is 2 and the forms are inseparably k-linked. We study whether the converse statements hold or not.

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• Types of Linkage of Quadratic Pfister Forms
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