Abhyankar's lemma
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Abhyankar's lemma
Abhyankar's lemma is not directly related to Abhyankar's conjecture.
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 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: Séminaire de Géométrie Algébriques du Bois-Marie 1960/61. Lecture Notes in Math. 224. Springer-Verlag 1971, page 279.
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