The Artin Reciprocity Law is a general theorem of number theory forming a central part of global class field theory, generalizing a long line of more concrete reciprocity statements including the law of quadratic reciprocity and the reciprocity laws of Eisenstein and Kummer. Established by Emil Artin across a series of papers in the 1920s, it provided a partial solution to Hilbert's ninth problem and remains one of the foundational results connecting abelian extensions of number fields to the arithmetic of the base field.
Facts
StatementFor an abelian Galois extension of global fields, the law gives a canonical isomorphism between the Galois group of the extension and a quotient of the idele class group of the base field, generalizing the classical quadratic reciprocity law and the reciprocity laws of Eisenstein and Kummer. 1 Proof YearArtin established the law across papers from 1924 to 1930; the raw wikitext's own References list dates the general reciprocity law paper itself to 1927, the year recorded here. Classification
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Source Artin Reciprocity Law (Wikipedia)
Sources
1. Artin Reciprocity Law (Wikipedia)
Wikimedia FoundationLead section, opening statement of the law
The Artin reciprocity law, which was established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of global class field theory.
References list, Artin's 1927 paper
Emil Artin (1927) "Beweis des allgemeinen Reziprozitätsgesetzes", Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 5: 353-363
Proved By: Emil Artin, Lead
The Artin reciprocity law, which was established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of global class field theory.
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