Quadratic forms of dimension 8 with trivial discriminant and Clifford algebra of index 4 (Q842358)

The new proof avoids the algebra-geometric methods of Izhboldin-Karpenko and Rost's description of 14-dimensional forms in \(I^3F\). It is more elementary but also much more computational. The main ingredients are algebras with involution, decomposability results, transfer from a quadratic etale extension and triality. A large part of the proofs is quoted from earlier papers and books. For experts the paper is quite interesting.