Artin conductor

In mathematics, the Artin conductor is a number or ideal associated to a character of a Galois group of a local or global field, introduced by Emil Artin (1930, 1931) as an expression appearing in the functional equation of an Artin L-function.
Local Artin conductors
Suppose that L is a finite Galois extension of the local field K, with Galois group G. If χ is a character of G, then the Artin conductor of χ is the number
where Gi is the i-th ramification group (in lower numbering), of order gi, and χ(Gi) is the average value of χ on Gi. By a result of Artin, the local conductor is an integer. If χ is unramified, then its Artin conductor is zero. If L is unramified over K, then the Artin conductors of all χ are zero.
The wild invariant or Swan conductor...