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

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.

Cited by in corpus (1)

• Linkage of Pfister forms over semi-global fields