Linkage of Pfister forms over semi-global fields

Linkage of Pfister forms over semi-global fields

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 th...

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Veröffentlicht in:Mathematische Zeitschrift 2024-11, Vol.308 (3), Article 41
1. Verfasser: Daans, Nicolas
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description 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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title Linkage of Pfister forms over semi-global fields
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