Local Symbols and Existence Theorem
Let K be a field, Ks a separable closure of K, and let G = G(Ks/K). If χ is a character of G— i.e., an element of H1(G,Q/Z) then δχ is an element of H2(G, Z). If b ∈ K*, the cup product b. δχ is an element of the Brauer group H2(G, Ks*) = Bk. We denote this element by the symbol (χ,b).
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