Isotropy indices of Pfister multiples in characteristic 2

Abstract

Let F be a field of characteristic 2, π an n-fold bilinear Pfister form over F and φ an arbitrary quadratic form over F. In this note, we investigate Witt index, defect, total isotropy index and higher isotropy indices of φ and $\pi \otimes \phi$ and prove relations among the indices of these two forms over certain field extensions.