In algebraic number theory, through completion, the study of ramification of a prime ideal can often be reduced to the case of local fields where a more detailed analysis can be carried out with the aid of tools such as ramification groups. In this article, a local field is non-archimedean and has finite residue field. == Unramified extension == Let L / K {\displaystyle L/K} be a finite Galois extension of nonarchimedean local fields with finite residue fields ℓ /...