On the generic splitting of quadratic forms in characteristic 2

In [9] and [10] Knebusch established the basic facts of generic splitting theory of quadratic forms over a field of characteristic different from 2. This paper is related to [11] and [13] where Knebusch and Rehmann generalized partially this theory to a field of characteristic 2. More precisely, we begin with a complete characterization of quadratic forms of height 1 (we don't exclude anisotropic quadratic forms with quasi-linear part of dimension at least 1). This allows us to extend the notion of degree to characteristic 2. We prove some results on excellent forms and splitting tower of a quadratic form. Some results on quadratic forms of height 2 and degree 1 or 2 are given. Received: 6 March 2000; in final form: 5 October 2001 / Published online: 17 June 2002