Galois cohomology in degree 3 of function fields of curves over number fields

Let k be a field of characteristic not equal to 2. For n≥1, let Hn(k,Z/2) denote the nth Galois Cohomology group. The classical Tateʹs lemma asserts that if k is a number field then given finitely many elements α1, ,αn H2(k,Z/2), there exist a,b1, ,bn k* such that αi=(a) (bi), where for any λ k*, (λ) denotes the image of k* in H1(k,Z/2). In this paper we prove a higher dimensional analogue of the Tateʹs lemma.