This file is from a shared repository and may be used by other projects.
The description on its file description page there is shown below.
Summary
DescriptionClassExtensionAndArtinTransfer.png
English: This is the famous diagram whose commutativity was proved by Emil Artin. It reduces the number theoretic problem of the principalization of ideal classes of a base field K in an extension field L to the purely group theoretic task to determine the kernel of the transfer homomorphism T from the Galois group G=Gal(K'/K) to the Galois group H=Gal(L'/L),
where K', resp. L', denote maximal abelian extensions of K, resp. L. The horizontal arrows denote the reciprocity isomorphisms between class groups and Galois groups, mapping the class of a prime ideal p to the Frobenius automophism of p. The map j is the class extension homomorphism from K to L.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse
Original upload log
The original description page was here. All following user names refer to en.wikipedia.