Hasse_invariant_of_a_quadratic_form
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.[1]
It may also be viewed as the second Stiefel–Whitney class of Q.