Tamagawa numbers

E685697

arithmetic invariant invariant of algebraic groups invariant of elliptic curves number theoretic invariant

Tamagawa numbers are arithmetic invariants attached to algebraic groups or elliptic curves that measure certain volume or local factor contributions in number theory, notably appearing in the Birch and Swinnerton-Dyer conjecture.

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All labels observed (1)

Label	Occurrences
Tamagawa numbers canonical	1

How this entity was disambiguated

This entity first appeared as the object of triple T7743537 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Tamagawa numbers
Context triple: [Birch and Swinnerton-Dyer Conjecture, relatesConcept, Tamagawa numbers]

A. Namba
Namba is a major commercial and entertainment district in Osaka, Japan, known for its bustling nightlife, shopping, and iconic neon-lit streets.
B. Namba Marui
Namba Marui is a major Marui department store and shopping complex located in Osaka’s bustling Namba district, known for its fashion, dining, and entertainment options.
C. Temwaiku
Temwaiku is a village and district within South Tarawa in Kiribati, known as one of the populated islets forming the country's capital area.
D. Namba Grand Kagetsu
Namba Grand Kagetsu is a famous comedy theater in Osaka, Japan, known as a central venue for Yoshimoto Kogyo’s manzai and variety performances.
E. Eightfold Way
The Eightfold Way is a classification scheme for hadrons in particle physics that organizes them into symmetry-based groups, laying the groundwork for the quark model.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Tamagawa numbers
Target entity description: Tamagawa numbers are arithmetic invariants attached to algebraic groups or elliptic curves that measure certain volume or local factor contributions in number theory, notably appearing in the Birch and Swinnerton-Dyer conjecture.

A. Namba
Namba is a major commercial and entertainment district in Osaka, Japan, known for its bustling nightlife, shopping, and iconic neon-lit streets.
B. Namba Marui
Namba Marui is a major Marui department store and shopping complex located in Osaka’s bustling Namba district, known for its fashion, dining, and entertainment options.
C. Temwaiku
Temwaiku is a village and district within South Tarawa in Kiribati, known as one of the populated islets forming the country's capital area.
D. Namba Grand Kagetsu
Namba Grand Kagetsu is a famous comedy theater in Osaka, Japan, known as a central venue for Yoshimoto Kogyo’s manzai and variety performances.
E. Eightfold Way
The Eightfold Way is a classification scheme for hadrons in particle physics that organizes them into symmetry-based groups, laying the groundwork for the quark model.
F. None of above. chosen

Statements (49)

Predicate	Object
instanceOf	arithmetic invariant ⓘ invariant of algebraic groups ⓘ invariant of elliptic curves ⓘ number theoretic invariant ⓘ
appearsAsFactorIn	BSD formula denominator ⓘ volume computations for arithmetic quotients ⓘ
appearsIn	Birch and Swinnerton-Dyer formula ⓘ linked to: Birch and Swinnerton-Dyer Conjecture formula for the leading term of the L-function of an elliptic curve at s = 1 ⓘ mass formulae for algebraic groups ⓘ
associatedWith	algebraic group over a number field ⓘ elliptic curve over a number field ⓘ
conjecturallyRelatedTo	finiteness of Tate–Shafarevich groups ⓘ rank of elliptic curves ⓘ
context	Langlands program ⓘ arithmetic of reductive groups ⓘ automorphic forms ⓘ
definedOver	number fields ⓘ
definedUsing	adelic quotient of an algebraic group ⓘ product of local measures ⓘ
describedAs	volume of adelic points modulo rational points ⓘ
field	algebraic geometry ⓘ arithmetic geometry ⓘ number theory ⓘ
historicalDevelopment	introduced in the mid-20th century ⓘ
namedAfter	Toshio Tamagawa NERFINISHED ⓘ
property	factorizes as a product of local contributions ⓘ invariant under isomorphism of algebraic groups over a number field ⓘ
relatedTo	Galois cohomology ⓘ Haar measure ⓘ Tamagawa measure ⓘ linked to: Haar measure Weil’s adelic formalism ⓘ linked to: Tate's thesis adelic points ⓘ cohomology of algebraic groups ⓘ local factors of L-functions ⓘ rational points ⓘ
specialCase	Tamagawa number of a semisimple algebraic group ⓘ linked to: Adeles and Algebraic Groups Tamagawa number of a torus ⓘ Tamagawa number of an elliptic curve ⓘ
studiedBy	André Weil ⓘ Goro Shimura ⓘ John Tate ⓘ Yutaka Taniyama ⓘ
takesValuesIn	positive rational numbers ⓘ
usedIn	Birch and Swinnerton-Dyer conjecture ⓘ linked to: Birch and Swinnerton-Dyer Conjecture Tamagawa measure theory ⓘ Weil conjectures for algebraic groups ⓘ linked to: Weil conjectures arithmetic of elliptic curves ⓘ rational points on abelian varieties ⓘ study of L-functions ⓘ

How these facts were elicited

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Birch and Swinnerton-Dyer Conjecture → relatesConcept → Tamagawa numbers ⓘ

All labels observed (1)

How this entity was disambiguated Show

Statements (49)

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Referenced by (1)

How this entity was disambiguated

How these facts were elicited