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Linkage of Pfister forms
over $\mathbb C(x_1,\ldots,x_n)$
Adam Chapman and Jean-Pierre Tignol |
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Vol. 4 (2019), No. 3, 521–524
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Abstract |
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We prove the existence of a set of cardinality of -fold Pfister forms over which do not share a common -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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Keywords
quadratic forms, linkage, rational function fields
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Mathematical Subject Classification 2010
Primary: 11E81
Secondary: 11E04, 19D45
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Milestones
Received: 6 March 2019
Revised: 21 May 2019
Accepted: 11 June 2019
Published: 17 December 2019
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Authors |
| Adam Chapman | |
| Department of Computer Science Tel-Hai Academic College Upper Galilee Israel |
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| Jean-Pierre Tignol | |
| ICTEAM Institute UCLouvain Louvain-la-Neuve Belgium |
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