Function Fields of Pfister Neighbors

✍ Scribed by H. Ahmad; J. Ohm

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 585 KB
• Volume: 178
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1995.1371

✦ Synopsis

A quadratic form (Q) is called a special Pfister neighbor if (Q) is similar to a form of the shape (P_{0} \perp a P_{1}), where (P_{0}) is Pfister, (a \in k^{*}), and (P_{1}) is a nonzero subform of (P_{0}). The Pfister form (P_{0} \perp a P_{0}), 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 (\leq 4) is a special Pfister neighbor; and there exists an example with (\operatorname{dim} P=16) and (\operatorname{codim} Q=5) which is not special. Special Pfister neightors 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. (c) 1995 Academic Press, Inc.