Vol. 4, No. 3, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
Ethics Statement
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
Author Index
To Appear
 
Other MSP Journals
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
Abstract

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.

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