Micro primes
In his book ``Class field theory'' [Springer Verlag Berlin (1986; Zbl 0587.12001)] the author develops class field theory on a group theoretical basis with a surprisingly easy definition of the reciprocity map using the characterization of this map by means of Durchkreuzung the given extension with a special extension, which in the local case is unramified and in the global case cyclotomic [see e.g. \textit{J. P. Serre}, Local class field theory, p. 145, in Algebraic Number Theory, Academic Press, London (1967; Zbl 0153.074)]. The definition of the reciprocity map by the author depends on the choice of a certain ``prime element''. In his present paper the author develops the concept of microprimes for a better understanding of the independence of the reciprocity map of the choice of the prime element. A microprime is a certain conjugacy class in a valued group. In this rather general setting one has a theory of decomposition groups of microprimes and other features known from algebraic number theory.
scientific article; zbMATH DE number 562481