Local Fields pp 204-222 | Cite as

Local Symbols and Existence Theorem

  • Jean-Pierre Serre
Part of the Graduate Texts in Mathematics book series (GTM, volume 67)


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).


Existence Theorem Galois Group Finite Index Residue Field Finite Extension 
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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Jean-Pierre Serre
    • 1
  1. 1.Collège de FranceParisFrance

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