- Turkish Journal of Mathematics
- Vol: 24 Issue: 1
- On the Metabelian Local Artin Map I: Galois Conjugation Law
On the Metabelian Local Artin Map I: Galois Conjugation Law
Authors : Kazım Ilhan Ikeda
Pages : 25-58
View : 9 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :It is proved that, for a (henselian) local field K and for a fixed Lubin-Tate splitting f over K, the metabelian local Artin map (?, K)f: B(K, f) \tilde{\rightarrow} Gal (K(ab)2 / K) satisfies the Galois conjugation law (\tilde{s}+(a), s (K))\tilde{s}f\tilde{s}-1 = \tilde{s}|K(ab)2 (a, K)f\tilde{s}-1|\tilde{s}(K(ab)2) for any a \in B(K, f), and for any embedding s : K \hookrightarrow Ksep, where \tilde{s} \in Aut (Ksep) is a fixed extension to Ksep of the embedding s : K \hookrightarrow Ksep.Keywords : local fields, metabelian extensions, metabelian local Artin map, non-abelian local class field theory.