In his Paper "Fields of u-invariant 9" Oleg Izhboldin points out that for a algebraic closed, finitely generated field $k$ we have $u(k)= 2^{cd(k)}$. In particular we have


$u(\mathbb{C}((t\_1),..(t\_n))) = 2^n$.


What do we get if we replace $\mathbb{C}$ with the p-adic numbers $\mathbb{Q}\_p$, which have $u(\mathbb{Q}\_p)=4$ ?


I think this question is unknown in general, are there any new results?



u-Invariants of p-adic function fields
My question has been answered positiv by David B. Leep in his publication


The u-invariant of p-adic function fields - Journal für die reine und angewandte Mathematik, Band 2013, Heft 679 (Jun 2013).


