2025/02/18 by Becher, Karim Johannes, Daans, Nicolas, Mehmeti, Vlerë · 1 citation
#11E04 #11E81 #12D15 #12J10 #14H05 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2502.13086
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.