Generalised quadratic forms and the u-invariant

Abstract

The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in characteristic 2 and investigate the relationships between them. We also investigate these invariants in the case of a quaternion algebra and in particular when this quaternion algebra is the unique quaternion division algebra over a field.