标题： 函数域在单变量中的u-不变量 显示英文标题

标题： The u-invariant of function fields in one variable

摘要： 域的u-不变量是该域上不可约二次扭形式的最大维数。 在本文中，我们得到了一个关于具有任意值群和剩余域特征不同于2的Henselian赋值域上单变量函数域的u-不变量的界限。 这推广了Harbater、Hartmann和Krashen的定理及其由Scheiderer的扩展。 他们的结果涵盖了赋值为离散的特殊情况。 显示英文摘要

摘要： 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.