Explicit Reciprocity Law for Lubin–Tate Formal Groups

In this article, using Fontaine’s ΦΓ–module theory, we give a new proof of Coleman’s explicit reciprocity law, which generalizes that of Artin–Hasse, Iwasawa andWiles, by giving a complete formula for the norm residue symbol on Lubin–Tate groups. The method used here is different from the classical ones and can be used to study the Iwasawa theory of crystalline representations.