Vol. 4, No. 3, 2019

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Linkage of Pfister forms over $\mathbb C(x_1,\ldots,x_n)$

Adam Chapman and Jean-Pierre Tignol

Vol. 4 (2019), No. 3, 521–524

We prove the existence of a set of cardinality 2n of n-fold Pfister forms over (x1,,xn) which do not share a common (n 1)-fold factor. This gives a negative answer to a question raised by Becher. The main tools are the existence of the dyadic valuation on the complex numbers and recent results on symmetric bilinear forms over fields of characteristic 2.

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quadratic forms, linkage, rational function fields
Mathematical Subject Classification 2010
Primary: 11E81
Secondary: 11E04, 19D45
Received: 6 March 2019
Revised: 21 May 2019
Accepted: 11 June 2019
Published: 17 December 2019
Adam Chapman
Department of Computer Science
Tel-Hai Academic College
Upper Galilee
Jean-Pierre Tignol
ICTEAM Institute