Chain Lemma, Quadratic Forms and Symbol Length

2023/04/15 by Chapman, Adam, Levin, Ilan
#11E04 #11E81 #15A66 (secondary) #16K20 (primary) #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2304.07644

Abstract

We want to bound the symbol length of classes in _2^m-1Br(F) which are represented by tensor products of 5 or 6 cyclic algebras of degree 2^m. The main ingredients are the chain lemma for quadratic forms, a form of a generalized Clifford invariant and Pfister's and Rost's descriptions of 12- and 14-dimensional forms in I³ F.

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