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Local field

In mathematics, a local field is a locally compact Hausdorff non-discrete topological field. Local fields find many applications in algebraic number theory, where they arise naturally as completions of global fields. Moreover, tools like integration and Fourier analysis are available for functions defined on local fields.

Measurement, Basic features of non-Archimedean local fields & Overview

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Overview

Module, absolute value, metric

Basic features of non-Archimedean local fields

Theory of local fields

Variant definitions

Higher-dimensional local fields

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Map overview Semantic statistics

Local field

Nodes69
Edges68
Triples34
Avg. degree1.97
Density0.028986
Components1

How this topic connects Entity context

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Local field

Top relations

related to Module, absolute value, metric · 7
Local field → As, First, Given, Haar, Specifically, The, This
related to Theory of local fields · 7
Local field → Galois, Hensel's, Hilbert, Hodge, Hodge-Tate, Langlands, This
related to Variant definitions · 5
Local field → Archimedean, Hausdorff, Research, Some, The
related to External links · 4
Local field → EMS Press, Encyclopedia, Local, Mathematics
related to Structure of the unit group · 3
Local field → Archimedean, Its, The
is a · 2
Local field → complete discrete valuation field whose residue field is an, locally compact Hausdorff non-discrete topological field
related to Basic features of non-Archimedean local fields · 2
Local field → Archimedean, For
related to Higher unit groups · 2
Local field → Archimedean, The
related to Higher-dimensional local fields · 1
Local field → Archimedean
see also · 1
Local field → Hensel's

Important terminology Word statistics

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Important terminology

local displaystyle field fields non-archimedean mathbb group finite residue characteristic valuation complete defined discrete unit absolute value metric called theory

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Local fieldis alocally compact Hausdorff non-discrete topological field0.90text
Local fieldis acomplete discrete valuation field whose residue field is an0.90text
Local fieldrelated to Basic features of non-Archimedean local fieldsFor0.60section
Local fieldrelated to Basic features of non-Archimedean local fieldsArchimedean0.60section
Local fieldrelated to External linksLocal0.60section
Local fieldrelated to External linksEncyclopedia0.60section
Local fieldrelated to External linksMathematics0.60section
Local fieldrelated to External linksEMS Press0.60section
Local fieldrelated to Higher unit groupsThe0.60section
Local fieldrelated to Higher unit groupsArchimedean0.60section
Local fieldrelated to Higher-dimensional local fieldsArchimedean0.60section
Local fieldrelated to Module, absolute value, metricGiven0.60section

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