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arXiv · 2502.13086

The u-invariant of function fields in one variable

Karim Johannes Becher·Nicolas Daans·Vlerë Mehmeti
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Abstract

The u-invariant of a field is the largest dimension of an anisotropic quadratic torsion form over the field. In this article we obtain a bound on the u-invariant of function fields in one variable over a henselian valued field with arbitrary value group and with residue field of characteristic different from 2. This generalises a theorem due to Harbater, Hartmann and Krashen and its extension due to Scheiderer. Their result covers the special case where the valuation is discrete. We further give a new proof of a theorem due to Parimala and Suresh bounding by 8 the u-invariant of a function field in one variable over any henselian discretely valued field of characteristic 0 with perfect residue field of characteristic 2.

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Karim Johannes Becher, Nicolas Daans, Vlerë Mehmeti. 2025-02-18. The u-invariant of function fields in one variable. https://arxiv.org/abs/2502.13086

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