Spaces of similarities. III: Function fields (Q1239222)

Continue the notation from the preceding two reviews. In this paper, the Pfister factor conjecture is proved for the cases \(\dim q = 2^m\), \(m\leq 5\), over an arbitrary field \(F\) (of characteristic not 2). The proof involves the generic splitting towers for quadratic forms developed by \textit{M. Knebusch}. If the field \(F\) is a global field, the conjecture is also proved for all forms over \(F\). These results are established more generally by different methods in a paper by the second author [Pac. J. Math. 69, 223--244 (1976; Zbl 0326.15015)].