Abhyankar's lemma
In mathematics, Abhyankar's lemma (named after Shreeram Shankar Abhyankar) allows one to kill tame ramification by taking an extension of a base field. More precisely, Abhyankar's lemma states that if "A", "B", "C" are local fields such that "A" and "B" are finite extensions of "C", with ramification indices "a" and "b", and "B" is tamely ramified over "C" and "b" divides "a", then the compositum "AB" is an unramified extension of "A".