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 H<SUP>n</SUP>(k, Z/Z) denote the nth Galois Cohomology group. The classical Tate's lemma asserts that if k is a number field then given finitely many elements , α<SUB>1</SUB>, ..., α<SUB>n</SUB>(k, Z/2), there exist a, b<SUB>1</SUB>..., b<SUB>n</SUB> ε such that a<SUB>i</SUB>= (a)∪(b<SUB>i</SUB>), where for any λε k*, (λ) denotes the image of k* in H<SUP>1</SUP>(k, Z/2). In this paper we prove a higher dimensional analogue of the Tate's lemma