Witt kernels of bi-quadratic extensions in characteristic 2

Abstract

Let κ be a field of characteristic 2. The author's previous results (Arch. Math. (1994)) are used to prove the excellence of quadratic extensions of κ. This in turn is used to determine the Witt kernel of a quadratic extension up to Witt equivalence. An example is given to show that Witt equivalence cannot be strengthened to isometry.