Academic Journal

Linkage of Pfister forms over ℂ(x1,…,xn)

Bibliographic Details
Title: Linkage of Pfister forms over ℂ(x1,…,xn)
Authors: Chapman, Adam, Tignol, Jean-Pierre
Contributors: UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique
Source: Annals of K-theory, Vol. 4, no.3, p. 521-524 (2019)
Ann. K-Theory 4, no. 3 (2019), 521-524
Publication Status: Preprint
Publisher Information: Mathematical Sciences Publishers, 2019.
Publication Year: 2019
Subject Terms: rational function fields, 11E81, 11E04, 19D45, 11E81, 0103 physical sciences, 11E04, FOS: Mathematics, 0101 mathematics, linkage, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 01 natural sciences, quadratic forms, 19D45
Description: In this note, we prove the existence of a set of $n$-fold Pfister forms of cardinality $2^n$ over $\mathbb{C}(x_1,\dots,x_n)$ 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 over fields of characteristic 2.
Document Type: Article
Other literature type
File Description: application/pdf
Language: English
ISSN: 2379-1691
2379-1683
DOI: 10.2140/akt.2019.4.521
DOI: 10.48550/arxiv.1903.02776
Access URL: http://arxiv.org/pdf/1903.02776
http://arxiv.org/abs/1903.02776
https://ui.adsabs.harvard.edu/abs/2019arXiv190302776C/abstract
https://arxiv.org/pdf/1903.02776
https://arxiv.org/abs/1903.02776
https://projecteuclid.org/journals/annals-of-k-theory/volume-4/issue-3/Linkage-of-Pfister-forms-over-mathbb-Cx_1ldotsx_n/10.2140/akt.2019.4.521.full
https://dial.uclouvain.be/pr/boreal/object/boreal:224032
https://msp.org/akt/2019/4-3/p06.xhtml
https://msp.org/akt/2019/4-3/akt-v4-n3-p06-s.pdf
https://hdl.handle.net/2078.1/224032
https://projecteuclid.org/euclid.akt/1578020478
Rights: arXiv Non-Exclusive Distribution
Accession Number: edsair.doi.dedup.....9b16a21a6b9c3c4ff41b75a40d3a0b10
Database: OpenAIRE
Description
ISSN:23791691
23791683
DOI:10.2140/akt.2019.4.521