Ahmed Laghribi: On the generic splitting of quadratic forms in characteristic 2

laghribi@euler.univ-artois.fr

Submission: 2000, Oct 3

In [8] and [9] Knebusch established the basic facts of generic splitting theory of quadratic forms over a field of characteristic not $2$. In [10], he generalized this theory to a field of characteristic $2$. This note is related to [3]. More precisely, we begin with a complete characterization of quadratic forms of height $1$ (in this note we don't exclude anisotropic quadratic forms with radical of dimension at least $1$). This allows us to extend the notion of degree in characteristic $2$. We prove some results on excellent forms and generic splitting tower of a quadratic form. Some results on quadratic forms of height $2$ and degree $1$ or $2$ are given.

1991 Mathematics Subject Classification: 11E04

Keywords and Phrases: quadratic forms, generic splitting

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