The Hilbert symbol for Lubin-Tate formal groups. II
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.
scientific article; zbMATH DE number 3916411