Different exponent
= Different exponent
{title2=$d_{\mathfrak P}=v_{\mathfrak P}(\mathfrak D_{E/K})$}
The different exponent at a <prime ideal> $\mathfrak P$ is its exponent in the <prime ideal factorization> of the <different ideal>. It equals the local different exponent of the corresponding extension of completions. The <different exponent and tame ramification> theorem detects unramified, tame, and wild behavior without assuming a <Galois extension>.