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Idele group

In number theory, the idele group is a way of packaging the multiplicative arithmetic of a global field at all of its completions at once, so that it contains the information of unique factorization as well as the data relating to units. Formally, the idele group of a global field K {\displaystyle K} is the restricted direct product A K × = ∏ v ′ K v ×…

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Overview

Definition

Motivation

Topology and Haar measure

Norm map and norm-one ideles

Class field theory

Hecke characters and L-functions

Further structure and proof sketches

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Idele group

Nodes44
Edges43
Triples31
Avg. degree1.95
Density0.045455
Components1

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Idele group

Top relations

related to Ideles of finite-dimensional algebras · 6
Idele group → As, For, Let, Since, The, There
related to Norm map and norm-one ideles · 6
Idele group → At, Choose, For, The, This, Thus
related to Definition · 4
Idele group → For, If, Let, The
related to Norms for field extensions · 4
Idele group → For, L/K, Let, These
related to Motivation · 3
Idele group → If, The, Thus
related to Relation with the ideal class group · 3
Idele group → For, Its, Let
related to Topology and Haar measure · 3
Idele group → Although, Instead, With
is a · 2
Idele group → group of invertible elements of the adele ring A K, way of packaging the multiplicative arithmetic of a global field at all of its completions at once

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Important terminology

displaystyle times idele group mathbb finite class field product places ideal mathcal topology number theory mathfrak local subgroup global alpha

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Idele groupis away of packaging the multiplicative arithmetic of a global field at all of its completions at once0.90text
Idele groupis agroup of invertible elements of the adele ring A K0.90text
Idele grouprelated to DefinitionLet0.60section
Idele grouprelated to DefinitionFor0.60section
Idele grouprelated to DefinitionIf0.60section
Idele grouprelated to DefinitionThe0.60section
Idele grouprelated to Ideles of finite-dimensional algebrasThe0.60section
Idele grouprelated to Ideles of finite-dimensional algebrasLet0.60section
Idele grouprelated to Ideles of finite-dimensional algebrasSince0.60section
Idele grouprelated to Ideles of finite-dimensional algebrasFor0.60section
Idele grouprelated to Ideles of finite-dimensional algebrasThere0.60section
Idele grouprelated to Ideles of finite-dimensional algebrasAs0.60section

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