Hasse invariant of a quadratic form (original) (raw)

In mathematics, the Hasse invariant (or Hasse–Witt invariant) of a quadratic form Q over a field K takes values in the Brauer group Br(K). The name "Hasse–Witt" comes from Helmut Hasse and Ernst Witt. The quadratic form Q may be taken as a diagonal form Σ aixi2. Its invariant is then defined as the product of the classes in the Brauer group of all the quaternion algebras (ai, aj) for i < j. This is independent of the diagonal form chosen to compute it. It may also be viewed as the second Stiefel–Whitney class of Q.