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2019 Linkage of Pfister forms over $\mathbb C(x_1,\ldots,x_n)$
Adam Chapman, Jean-Pierre Tignol
Ann. K-Theory 4(3): 521-524 (2019). DOI: 10.2140/akt.2019.4.521

Abstract

We prove the existence of a set of cardinality 2 n of n -fold Pfister forms over ( x 1 , , x n ) 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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Adam Chapman. Jean-Pierre Tignol. "Linkage of Pfister forms over $\mathbb C(x_1,\ldots,x_n)$." Ann. K-Theory 4 (3) 521 - 524, 2019. https://doi.org/10.2140/akt.2019.4.521

Information

Received: 6 March 2019; Revised: 21 May 2019; Accepted: 11 June 2019; Published: 2019
First available in Project Euclid: 3 January 2020

zbMATH: 07146019
MathSciNet: MR4043468
Digital Object Identifier: 10.2140/akt.2019.4.521

Subjects:
Primary: 11E81
Secondary: 11E04 , 19D45

Keywords: linkage , Quadratic forms , rational function fields

Rights: Copyright © 2019 Mathematical Sciences Publishers

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