Function Fields of Pfister Neighbors Original Research Article

A quadratic form Q is called a special Pfister neighbor if Q is similar to a form of the shape P0 perpendicular aP1, where P0 is Pfister, a set membership, variant k*, and P1 is a nonzero subform of P0. The Pfister form P0 perpendicular aP0, which is uniquely determined by Q, is called the associated Pfister form of Q. If P is an anisotropic Pfister form of dimension > 8, then every subform Q of P of codimension ≤ 4 is a special Pfister neighbor; and there exists an example with dim P = 16 and codim Q = 5 which is not special. Special Pfister neighbors of the same dimension and with the same associated Pfister form define the same function field, but there exists an example in dimension 5 which shows that such forms need not be similar.