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 $\sigma : K \hookrightarrow K^{sep}$.
Keywords
local fields, metabelian extensions, metabelian local Artin map, non-abelian local class field theory.
First Page
25
Last Page
58
Recommended Citation
İKEDA, KAZIM İLHAN (2000) "On the Metabelian Local Artin Map I: Galois Conjugation Law," Turkish Journal of Mathematics: Vol. 24: No. 1, Article 3. Available at: https://journals.tubitak.gov.tr/math/vol24/iss1/3
