Albrecht Pfister: Eine Bemerkung zum Normenresthomomorphismus h : K^*F/2 --> H^*(F,Z/2)

pfister@Mathematik.Uni-Mainz.DE

Submission: 2002, Mar 06

An elementary Galois theoretic proof is given for the fact: An element $b \in \dot{F}$ is a norm from the extension $F (\sqrt{a})$ iff $(a) \cup (b) = 0$ in $H^2 (F, \gz / 2)$. From this it follows easily that $h$ exists. Comments about other proofs and applications to quadratic forms conclude the paper.

2000 Mathematics Subject Classification:

Keywords and Phrases:

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