Arason invariant
In mathematics, the Arason invariant is a cohomological invariant associated to a quadratic form of even rank and trivial discriminant and Clifford invariant over a field k of characteristic not 2, taking values in H3. It was introduced by.
The Rost invariant is a generalization of the Arason invariant to other algebraic groups.Definition
Suppose that W is the Witt ring of quadratic forms over a field k and I is the ideal of forms of even dimension. The Arason invariant is a group homomorphism from I3 to the Galois cohomology group H3. It is determined by the property that on the 8-dimensional diagonal form with entries 1, –a, –b, ab, -c, ac, bc, -abc it is given by the cup product of the classes of a, b, c in H1 = k*/k*2. The Arason invariant vanishes on I4, and it follows from the Milnor conjecture proved by Voevodsky that it is an isomorphism from I3/I4 to H3.
