M/E23

The u-invariant of a field is the largest dimension of an anisotropic quadratic torsion form over the field. This field invariant was introduced by I. Kaplansky in 1953 and addapted to the study of real fields by R. Elman and T.Y. Lam in 1973. In 2009, D. Harbater, J. Hartmann, and D. Krashen obtained a bound on the u-invariant for nonreal function fields in one variable over a complete discretely valued field. In joint work with N. Daans and V. Mehmeti, we obtain a more general version of this result, namely for function fields of curves over a henselian valued field with arbitrary value group.

Karim Becher

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