This article deals with the
standard splitting of bilinear forms in characteristic 2. The first part is devoted to the
study of bilinear Pfister neighbors (the definition of such a bilinear form is slightly
different from the classical definition of a Pfister neighbor quadratic form). In the
second part, we introduce the degree invariant for bilinear forms and we prove that
for any integer d ≥ 0, the d-th power of the ideal of even dimensional bilinear forms
coincides with the set of bilinear forms of degree ≥ d (this is a positive answer to the
analogue of the degree conjecture for quadratic forms). In the third part, we
classify good bilinear forms of height 2, and we give information on the
possible dimensions of bilinear forms of height 2 which are not necessarily
good.
Keywords
symmetric bilinear form, function field of a bilinear form,
standard splitting of bilinear forms, bilinear Pfister
neighbors
