Abstract
Let 𝔽̄q be the algebraic closure of the finite field 𝔽q. Let 𝔊 be the group of continuous 𝔽̄q-automorphisms σ of the abelian closure of the series field 𝔽q((t)) such that σ(t) ∈ t𝔽q[[t]]×. The set 𝔽̄q [[t]]× is a group for the non-commutative Ore multiplication of the series (the ordinary multiplication twisted by the Frobenius map). In this paper, by means of the Koch–de Shalit reciprocity map, we construct a subgroup W of this group and an isomorphism ι of W onto 𝔊, which extends the Artin reciprocity map. Thus the Nottingham group can be described with Ore multiplication; this description gives rise to a larger interpretation of the Schmid local symbol and gives some information on its finite abelian subgroups. We study the behaviour of ι relative to ramification and norm mapping.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
