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Turkish Journal of Mathematics

DOI

-

Abstract

It is proved that, for a (henselian) local field $K$ and for a fixed Lubin-Tate splitting $\phi$ over $K$, the metabelian local Artin map (?, $K)_{\phi}: B(K, \phi) \tilde{\rightarrow} Gal (K^{(ab)^2} / K)$ satisfies the Galois conjugation law $$(\tilde{\sigma}^+(\alpha), \sigma (K))_{\tilde{\sigma}\phi\tilde{\sigma}^{-1}} = \tilde{\sigma} _{K^{(ab)^2}} (\alpha, K)_{\phi}\tilde{\sigma}^{-1} _{\tilde{\sigma}(K^{(ab)^2})}$$ for any $\alpha \in B(K, \phi)$, and for any embedding $\sigma : K \hookrightarrow K^{sep}$, where $\tilde{\sigma} \in$ Aut $(K^{sep}$) is a fixed extension to $K^{sep}$ of the embedding $\sigma : K \hookrightarrow K^{sep}$.

First Page

25

Last Page

58

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