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Adele ring

In number theory, the adele ring is a construction that combines all local versions of a global field into one object. For the rational numbers, these local versions include the real numbers and the fields of p {\displaystyle p} -adic numbers for all prime numbers p {\displaystyle p} . More generally, if K {\displaystyle K} is a global field, its adele…

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Overview

Definition

Motivation

Examples

Haar measure and Fourier analysis

Applications

Idele group

Further properties and proof sketches

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Map overview Semantic statistics

Adele ring

Nodes63
Edges62
Triples68
Avg. degree1.97
Density0.031746
Components1

How this topic connects Entity context

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Adele ring

Top relations

related to Tate's thesis and L-functions · 12
Adele ring → Adelic, Dirichlet, Fourier, Haar, Hecke, In Tate's, John Tate, Poisson, Riemann, The, Their, With
related to Class field theory · 7
Adele ring → Artin, At, Galois, Global, In, L/K, The
related to Motivation · 7
Adele ring → For, If, Minkowski, Minkowski's, More, Ostrowski's, The
related to Approximation and local-global principles · 5
Adele ring → Adelic, Hasse, In, The, Thus
related to Curves, divisors, and bundles · 4
Adele ring → For, In, One, Picard
related to Number fields · 4
Adele ring → At, Let, The, Thus
related to Rational adeles · 4
Adele ring → For, Ostrowski's, The, Thus
related to Serre duality on curves · 4
Adele ring → Adeles, If, Serre, Tate
related to Topology and main properties · 4
Adele ring → Equipped, For, If, The
is a · 3
Adele ring → construction that combines all local versions of a global field into one object, restricted product topology, union of all these open subrings

Important terminology Word statistics

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Important terminology

displaystyle mathbb ring adele group finite product field places restricted idele one global topology number compact adelic times local mathcal

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Adele ringis aconstruction that combines all local versions of a global field into one object0.90text
Adele ringis arestricted product topology0.90text
Adele ringis aunion of all these open subrings0.90text
semisimple groupsinstance offor suitable groups0.80text
and also for GL ninstance offor suitable groups0.80text
Adele ringrelated to Adeles of vector spaces and algebrasLet0.60section
Adele ringrelated to Adeles of vector spaces and algebrasFor0.60section
Adele ringrelated to Adeles of vector spaces and algebrasThe0.60section
Adele ringrelated to Approximation and local-global principlesThe0.60section
Adele ringrelated to Approximation and local-global principlesThus0.60section
Adele ringrelated to Approximation and local-global principlesAdelic0.60section
Adele ringrelated to Approximation and local-global principlesHasse0.60section

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