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arXiv · 1903.02776

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

Adam Chapman·Jean-Pierre Tignol
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Abstract

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.

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Adam Chapman, Jean-Pierre Tignol. 2019-03-07. Linkage of Pfister forms over $\mathbb{C}(x_1,\ldots,x_n)$. https://doi.org/10.2140/akt.2019.4.521

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