Discretely valued fields with infinite u-invariant: Research announcement (Q750491)

The \(u\)-invariant of a field \(F\) is the supremum of dimensions of anisotropic quadratic forms over \(F\). If the supremum is not finite and there exists an infinite dimensional anisotropic quadratic form over \(F\), the \(u\)-invariant is said to be strongly infinite. The authors consider the question if there exists a field with infinite but not strongly infinite \(u\)-invariant. A condition for the \(u\)-invariant to be strongly infinite is stated for a discretely valued field. Several consequences of this result are mentioned. Proofs will appear elsewhere.