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Class formation

In mathematics, a class formation is a topological group acting on a module satisfying certain conditions. Class formations were introduced by Emil Artin and John Tate to organize the various Galois groups and modules that appear in class field theory.

Art, Definitions & Weil group

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Overview

Definitions

Examples

The first inequality

The second inequality

The Brauer group

Tate's theorem and the Artin map

The Takagi existence theorem

Weil group

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Class formation

Nodes44
Edges43
Triples72
Avg. degree1.95
Density0.045455
Components1

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Class formation

Top relations

related to References · 45
Class formation → Amer, American Mathematical Society, AMS Chelsea Publishing, André, Artin, Automorphic, Berlin, Class, Emil, Graduate Texts, ISBN, ISSN, Japan, Jean-Pierre, John, Journal, L-functions Part, Local, Lock-gray-alt-2, Lock-green
related to Examples · 9
Class formation → Archimedean, Finite, G-action, Galois, Global, Laurent, Local, Non-archimedean, The
related to The Brauer group · 8
Class formation → An, Brauer, E/F, H1, H2, In, The, The Brauer
related to Weil group · 8
Class formation → AF, E/F, Galois, H2, If E/F, Langlands, The Weil, Weil
is a · 2
Class formation → formation such that for every normal layer E/FH1, topological group acting on a module satisfying certain conditions

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Important terminology

group class field formation fields theory h2 groups local galois theorem finite cyclic inequality second extensions artin first module layer

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Class formationis atopological group acting on a module satisfying certain conditions0.90text
Class formationis aformation such that for every normal layer E/FH10.90text
Class formationrelated to ExamplesThe0.60section
Class formationrelated to ExamplesArchimedean0.60section
Class formationrelated to ExamplesFinite0.60section
Class formationrelated to ExamplesG-action0.60section
Class formationrelated to ExamplesGalois0.60section
Class formationrelated to ExamplesLocal0.60section
Class formationrelated to ExamplesLaurent0.60section
Class formationrelated to ExamplesNon-archimedean0.60section
Class formationrelated to ExamplesGlobal0.60section
Class formationrelated to ReferencesLock-green0.60section

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