8 research outputs found
Quadratic forms of dimension 8 with trivial discrimiand and Clifford algebra of index 4
Izhboldin and Karpenko proved in 2000 that any quadratic form of dimension 8
with trivial discriminant and Clifford algebra of index 4 is isometric to the
transfer, with respect to some quadratic \'etale extension, of a quadratic form
similar to a 2-fold Pfister form. We give a new proof of this result, based on
a theorem of decomposability for degree 8 and index 4 algebras with orthogonal
involution