Modularity theorem

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History

Yutaka Taniyama Algebraic number theory Tokyo Nikkō Set of 36 unsolved problems

14 related topics

Statement

Theorem Rational map Integer Coefficients Classical modular curve

15 related topics

Example

Modular functions Meromorphic Upper half-plane Galois representations Yves Hellegouarch

8 related topics

Generalizations

Robert Langlands Automorphic form Automorphic representation Arithmetic algebraic geometry Number field

6 related topics

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Conjectured by: Yutaka Taniyama Goro Shimura
Conjectured in: 1957
Consequences: Fermat's Last Theorem
Field: Number theory
First proof by: Christophe Breuil Brian Conrad Fred Diamond Richard Taylor
First proof in: 2001

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Generalizations

Example

Modular functions Modular function
Meromorphic
Upper half-plane
Galois representations Galois representation
Yves Hellegouarch Yves Hellegouarch?action=edit&redlink=1
Fr Yves Hellegouarch
Hellegouarch–Frey curves Frey curve
Kenneth Ribet

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Nodes60

Edges59

Triples24

Avg. degree1.97

Density0.033333

Components1

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Modularity theorem

Top relations

related to Generalizations · 8

Modularity theorem → Freitas, In, Le Hung, Most, Robert Langlands, Siksek, The, The Langlands

related to Related statements · 5

Modularity theorem → Dirichlet, L-series, The, The L-series, To

related to Statement · 4

Modularity theorem → If, The, This, X0

Conjectured by · 1

Modularity theorem → Yutaka Taniyama Goro Shimura

Conjectured in · 1

Modularity theorem → 1957

Consequences · 1

Modularity theorem → Fermat's Last Theorem

Field · 1

Modularity theorem → Number theory

First proof by · 1

Modularity theorem → Christophe Breuil Brian Conrad Fred Diamond Richard Taylor

First proof in · 1

Modularity theorem → 2001

is a · 1

Modularity theorem → special case of more general conjectures due to Robert Langlands

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Important terminology

elliptic theorem conjecture modular modularity curve taniyama shimura curves flt weil proof number theory taylor proved conductor richard level form

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Modularity theorem	Conjectured by	Yutaka Taniyama Goro Shimura	1.00	infobox
Modularity theorem	Conjectured in	1957	1.00	infobox
Modularity theorem	Consequences	Fermat's Last Theorem	1.00	infobox
Modularity theorem	Field	Number theory	1.00	infobox
Modularity theorem	First proof by	Christophe Breuil Brian Conrad Fred Diamond Richard Taylor	1.00	infobox
Modularity theorem	First proof in	2001	1.00	infobox
Modularity theorem	is a	special case of more general conjectures due to Robert Langlands	0.90	text
Modularity theorem	related to Generalizations	The	0.60	section
Modularity theorem	related to Generalizations	Robert Langlands	0.60	section
Modularity theorem	related to Generalizations	The Langlands	0.60	section
Modularity theorem	related to Generalizations	Most	0.60	section
Modularity theorem	related to Generalizations	In	0.60	section

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Modularity theorem

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Modularity theorem

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