The Hilbert symbol for Lubin-Tate formal groups. II
type: Item
instance of: scholarly article
title: The Hilbert symbol for Lubin-Tate formal groups. II
zbMATH Open document ID: 0574.12016
DOI: 10.1007/BF02105100
author: I. B. Fesenko
author: S. V. Vostokov
published in: Journal of Soviet Mathematics
publication date: 1985-01-01T00:00:00Z
review text: This is the second part of an investigation of an explicit reciprocity law for the Hilbert symbol in Lubin-Tate extensions \(K/K_ 0\) with arbitrary residue characteristic p [see the first author, ibid. 27, 2885- 2901 (1984); translation from Zap. Nauchn. Semin Leningr. Otd. Mat. Inst. Steklova 114, 77-95 (1982; Zbl 0497.14019)]. Let F be the formal group law, \(\Pi_ 0\) be a prime element of \(K_ 0\), \({\mathfrak p}\) the prime ideal of K, F(\({\mathfrak p})\) the group which as a set is equal to \({\mathfrak p}\) with the group law given by F and let \({\mathcal H}_ n\) be the kernel of the isogeny \([\Pi^ n_ 0]\). Then the Hilbert symbol is a pairing \(K^{\times}\times F({\mathfrak p})\to {\mathcal H}_ n\). This paper contains the proof that the explicit pairing of Vostokov in the first part is identical with the Hilbert symbol.
Mathematics Subject Classification ID: 11S31
Mathematics Subject Classification ID: 14L05
zbMATH DE Number: 3916411
zbMATH Keywords: p-adic formal Lubin-Tate group
zbMATH Keywords: explicit reciprocity law
zbMATH Keywords: Hilbert symbol
zbMATH Keywords: isogeny
MaRDI profile type: Publication
cites work: Q4195041
cites work: Canonical decomposition in the group of points of a formal Lubin-Tate group
cites work: Q3941531
cites work: The Hilbert symbol for Lubin-Tate formal groups. I
cites work: Sur les lois de réciprocité explicites. I.
cites work: Zum expliziten Reziprozitätsgesetz von I. R. Šafarevič
full work available at URL: https://doi.org/10.1007/bf02105100
OpenAlex ID: W2319231993
description: scientific article; zbMATH DE number 3916411