Fields of characteristic 2 with prescribed u-invariants (Q749614)

For a field F of characteristic 2, the following invariants are considered: \[ u(F)=\sup \{\dim q|\;q\text{ anisotropic nonsingular quadratic form over }F\} \] \[ \hat u(F)=\sup \{\dim q|\;q\text{ anisotropic quadratic form over }F.\}. \] The methods Merkurjev used to construct fields of characteristic not 2 with arbitrary even u-invariant are adapted to the characteristic 2 case in the present paper, and are used to construct the following kind of examples in characteristic 2: 1) a field F with \(u(F)=\hat u(F)=6\). 2) for any integers n,m such that \(2^ m\geq 2n\geq 4\) and \(m\geq n-1\), a field F with \(u(F)=2n\) and \(\hat u(F)=2^ m\). 3) for any integer \(n\geq 2\), a field F with \(u(F)=2n\) and \(\hat u(F)=\infty\).