Ramification group

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Ramification theory of valuations

Mathematics Extensions Valuation Field Extension

23 related topics

Ramification groups in lower numbering

Hensel's lemma Primitive element theorem Trivial Inertia subgroup Splitting of prime ideals

16 related topics

Ramification groups in upper numbering

Absolute Galois group Hasse–Arf theorem Artin isomorphism

3 related topics

Overview

Number theory Local class field theory Filtration Galois group Local field

6 related topics

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Overview

Number theory
Local class field theory
Filtration Filtration (mathematics)
Galois group
Local field
Ramification Ramification (mathematics)

Ramification theory of valuations

Mathematics
Extensions Extension of a valuation
Valuation Valuation (algebra)
Field Field (mathematics)
Extension Field extension
Galois extension
Valued field
Finite Finite extension
Equivalence Equivalence of valuations
Classes Equivalence class
Representative Representative (mathematics)
Composition Function composition
Automorphism
Transitive Transitive action
Stabilizer subgroup
Subgroup
Maximal ideal Maximal ideal of a valuation
Valuation ring Valuation ring of a valuation
Act trivially Trivial action
Residue field Residue field of a valuation
Normal subgroup
Reduced ramification index Reduced ramification index of an extension of valuations
Relative degree Relative degree of an extension of valuations

Ramification groups in lower numbering

Hensel's lemma
Primitive element theorem
Trivial Trivial group
Inertia subgroup
Splitting of prime ideals Splitting of prime ideals in Galois extensions
Wild inertia subgroup Wild inertia subgroup?action=edit&redlink=1
Unramified Unramified extension
Tamely ramified
P-group
Solvable Solvable group
Different Different ideal
Lazard Michel Lazard
Lie algebra
Cyclotomic extension
Root of unity
Unit Unit (ring theory)

Ramification groups in upper numbering

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Nodes53

Edges52

Triples71

Avg. degree1.96

Density0.037736

Components1

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Ramification group

Top relations

related to References · 44

Ramification group → Academic Press, Algebraic, Algebraische Zahlentheorie, American Mathematical Society, Berlin, Cambridge, Cambridge University Press, Conrad, Fields Institute, Fröhlich, Galois, Graduate Texts, Greenberg, Grundlehren, Higher, In Cassels, International Mathematical Union, ISBN, Jean-Pierre, Jürgen

related to Herbrand's theorem · 10

Ramification group → Arf, G/H, Galois, H/H, Hasse, Herbrand's, It, L/F, The, This

related to Ramification groups in lower numbering · 8

Ramification group → As, Galois, Hensel's, L/K, Ramification, Then, This, We

related to Ramification groups in upper numbering · 8

Ramification group → Define, If, In, It, Leftrightarrow, Note, The, Then

related to Example: the cyclotomic extension · 1

Ramification group → The

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displaystyle ramification group extension galois groups geq field filtration theory -1 subgroup local numbering upper extensions finite zbl phi isbn

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Ramification group	related to Example: the cyclotomic extension	The	0.60	section
Ramification group	related to Herbrand's theorem	Herbrand's	0.60	section
Ramification group	related to Herbrand's theorem	H/H	0.60	section
Ramification group	related to Herbrand's theorem	G/H	0.60	section
Ramification group	related to Herbrand's theorem	L/F	0.60	section
Ramification group	related to Herbrand's theorem	This	0.60	section
Ramification group	related to Herbrand's theorem	Galois	0.60	section
Ramification group	related to Herbrand's theorem	The	0.60	section
Ramification group	related to Herbrand's theorem	Hasse	0.60	section
Ramification group	related to Herbrand's theorem	Arf	0.60	section
Ramification group	related to Herbrand's theorem	It	0.60	section
Ramification group	related to Ramification groups in lower numbering	Ramification	0.60	section

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Ramification theory of valuations

Ramification groups in lower numbering

Ramification groups in upper numbering

Overview

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Overview

Ramification theory of valuations

Ramification groups in lower numbering

Ramification groups in upper numbering

Advanced semantic analysis

Map overview Semantic statistics

Ramification group

How this topic connects Entity context

Ramification group

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges