Some generalizations of Springer’s theorem in characteristic two

Abstract

It is shown that an anisotropic [Formula: see text]-fold system of hermitian forms over a quaternion algebra in characteristic two remains anisotropic over all odd degree extensions of the base field. It is also shown that an anisotropic orthogonal involution on a central simple algebra of co-index 3 in characteristic two is anisotropic over any odd degree extension of the ground field.