On Kato and Kuzumaki’s properties for the Milnor K₂ of function fields of p-adic curves

Let K be the function field of a curve C over a p-adic field k. We prove that, for each n, d ≥ 1 and for each hypersurface (Formula present) of degreedwithd2 ≤ n, the second Milnor K-theory group of K is spanned by the images of the norms coming from finite extensions L of K over which Z has a rational point. When the curve C has a point in the maximal unramified extension of k, we generalize this result to hypersurfaces (Formula present) of degree d with d ≤ n.