On fields of \(u\)-invariant 4
The main result of this paper is as follows: Theorem 3.1 Assume that \(u(F(\sqrt {-1}))=4\). A necessary and sufficient condition to have that \(u(F)\leq 4\) is that, for any \(a\in D_F(3)\) and \(d\in D_F(2)\), the form \(\langle 1,1,-a,-ad\rangle\) is universal over \(F\). This strengthens and generalizes an old result of the reviewer (from the year 1981). The proof is short and elementary modulo standard theorems on quadratic forms over fields. Some related results are also proved. But the main conjecture remains still open: Is it true that \(u(F)\leq 4\) for any field \(F\) of transcendence degree 2 over \(\mathbb{R}\)?
scientific article; zbMATH DE number 5013995