 | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (May 2024) (Learn how and when to remove this message) |
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.
See also
References
- Cornell, Gary (1982), "On the Construction of Relative Genus Fields", Transactions of the American Mathematical Society, 271 (2): 501–511, doi:10.2307/1998895, JSTOR 1998895. Theorem 3, page 504.
- Gold, Robert; Madan, M. L. (1978), "Some applications of Abhyankar's lemma", Mathematische Nachrichten, 82: 115–119, doi:10.1002/mana.19780820112.
- Grothendieck, A. (1971), Revêtements étales et groupe fondamental (SGA 1, Séminaire de Géométrie Algébriques du Bois-Marie 1960/61), Lecture Notes in Mathematics, vol. 224, Springer-Verlag, arXiv:math.AG/0206203, p. 279.
- Narkiewicz, Władysław (2004), Elementary and analytic theory of algebraic numbers, Springer Monographs in Mathematics (3rd ed.), Berlin: Springer-Verlag, p. 229, ISBN 3-540-21902-1, Zbl 1159.11039.
 | This abstract algebra-related article is a stub. You can help Misplaced Pages by expanding it. |