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".

References

*Gary Cornell [http://links.jstor.org/sici?sici=0002-9947%28198206%29271%3A2%3C501%3AOTCORG%3E2.0.CO%3B2-T "On the Construction of Relative Genus Fields"] Theorem 3, page 504. Transactions of the American Mathematical Society, Vol. 271, No. 2. (Jun., 1982), pp. 501-511.
*Gold, Robert; Madan, M. L. "Some applications of Abhyankar's lemma." Math. Nachr. 82 (1978), 115-119.
*A. Grothendieck: [http://www.arxiv.org/abs/math.AG/0206203 "Séminaire de Géométrie Algébriques du Bois-Marie 1960/61."] Lecture Notes in Math. 224. Springer-Verlag 1971, [http://modular.fas.harvard.edu/sga/sga/1/1t_279.html page 279] .