On the scope of validity of the norm limitation theorem for quasilocal fields

Details On the scope of validity of the norm limitation theorem for quasilocal fields On the scope of validity of the norm limitation theorem for quasilocal fields

2005-11-23

arxiv.org/abs/math/0511587v1

Mathematics

Rings and Algebras

20 pages, Plain Tex

Scientific paper

Let $E$ be a quasilocal field, $R/E$ a finite separable extension, and $R _{\rm ab}$ the maximal abelian subextension of $E$ in $R$. The main result of this paper shows that the norm groups $N(R/E)$ and $N(R_{\rm ab}/E)$ are equal, if the natural Brauer group homomorphism Br$(E) \to $ Br$(L)$ is surjective, for every finite extension $L$ of $E$. The paper proves in a strong form that the surjectivity of the homomorphisms Br$(E) \to $ Br$(L)$ is essential.

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