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("k",Z/2Z). It was introduced by .
The Rost invariant is a generalization of the Arason invariant to other algebraic groups.
Definition.
Suppose that "W"("k") 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 "I"3 to the Galois cohomology group H3("k",Z/2Z). It is determined by the property that on the 8-dimensional diagonal form with entries 1, –"a", –"b", "ab", -"c", "ac", "bc", -"abc" (the 3-fold Pfister form«"a","b","c"») it is given by the cup product of the classes of "a", "b", "c" in H1("k",Z/2Z) = "k"*/"k"*2. The Arason invariant vanishes on "I"4, and it follows from the Milnor conjecture proved by Voevodsky that it is an isomorphism from "I"3/"I"4 to H3("k",Z/2Z).