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arXiv · 2402.10826

Linkage of Pfister forms over semi-global fields

Nicolas Daans
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Abstract

We study linkage of $(d+1)$-fold quadratic Pfister forms over function fields in one variable over a henselian valued field of 2-cohomological dimension $d$. Specifically, we characterise this property in terms of linkage of quadratic Pfister forms over function fields over the residue field of the henselian valued field; in full generality in characteristic different from 2, and for most complete discretely valued fields in characteristic 2. As an application, we obtain a proof that $(d+2)$-fold quadratic Pfister forms over function fields in one variable over a $d$-dimensional higher local field are linked.

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Nicolas Daans. 2024-02-16. Linkage of Pfister forms over semi-global fields. https://doi.org/10.1007/s00209-024-03598-2

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