Differential forms, linked fields, and the u-invariant

作者：Chapman Adam^*; Dolphin Andrew

来源：ARCHIV DER MATHEMATIK, 2017, 109(2): 133-142.

DOI：10.1007/s00013-017-1059-7

• Differential forms
• Quadratic forms
• Linked fields
• u-Invariant
• Fields of finite characteristic

We associate an Albert form to any pair of cyclic algebras of prime degree p over a field F with char(F) = p which coincides with the classical Albert form when p = 2. We prove that if every Albert form is isotropic, then H-4(F) = 0. As a result, we obtain that if F is a linked field with char(F) = 2, then its u-invariant is either 0, 2, 4, or 8.

• 出版日期2017-8