The $u$-invariant of the function fields of $p$-adic curves

Abstract

The $u$-invariant of a field is the maximum dimension of ansiotropic quadratic forms over the field. It is an open question whether the $u$-invariant of function fields of $p$-adic curves is $8$. In this paper, we answer this question in the affirmative for function fields of nondyadic $p$-adic curves.