## Nonabelian local reciprocity maps.(English)Zbl 1039.11085

Miyake, Katsuya (ed.), Class field theory – its centenary and prospect. Proceedings of the 7th MSJ International Research Institute of the Mathematical Society of Japan, Tokyo, Japan, June 3–12, 1998. Tokyo: Mathematical Society of Japan (ISBN 4-931469-11-6/hbk). Adv. Stud. Pure Math. 30, 63-78 (2001).
The author constructs non-Abelian reciprocity maps for arithmetically profinite Galois extensions $$L/F$$ of local fields. The Neukirch-Iwasawa norm map $${\mathcal N}:\text{Gal}(L/F)\to U^\lozenge$$, where $$U^\lozenge$$ is a certain subquotient of the unit group of the field of norms, and the Hazelwinkel homomorphism is generalized to give an explicit inverse $${\mathcal H}$$ of $${\mathcal N}$$. These constructions encompass both the metabelian class field theory of Koch and de Shalit, and the soluble theory of Gurevich.
For the entire collection see [Zbl 0968.00031].

### MSC:

 11S31 Class field theory; $$p$$-adic formal groups