Adeles and Algebraic Groups
E244838
"Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Adeles and Algebraic Groups canonical | 1 |
| Tamagawa number of a semisimple algebraic group | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2228030 — 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: Adeles and Algebraic Groups Context triple: [André Weil, notableWork, Adeles and Algebraic Groups]
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A.
Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem)
Noether’s AF+BG theorem is a foundational result in algebraic geometry that provides conditions under which a polynomial vanishing on the intersection of two plane curves can be expressed as a linear combination of their defining equations.
-
B.
Noether's problem
Noether's problem is a fundamental question in invariant theory and field theory that asks whether the fixed field of a finite group acting on a rational function field is itself a purely transcendental (rational) extension.
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C.
Hilbert’s irreducibility theorem
Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
-
D.
Hilbert’s twelfth problem
Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
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E.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
- 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: Adeles and Algebraic Groups Target entity description: "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
-
A.
Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem)
Noether’s AF+BG theorem is a foundational result in algebraic geometry that provides conditions under which a polynomial vanishing on the intersection of two plane curves can be expressed as a linear combination of their defining equations.
-
B.
Noether's problem
Noether's problem is a fundamental question in invariant theory and field theory that asks whether the fixed field of a finite group acting on a rational function field is itself a purely transcendental (rational) extension.
-
C.
Hilbert’s irreducibility theorem
Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
-
D.
Hilbert’s twelfth problem
Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
-
E.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ |
| aimsTo |
provide a systematic treatment of algebraic groups over adeles
ⓘ
unify local and global methods in number theory using adeles ⓘ |
| author | André Weil ⓘ |
| contributor | André Weil ⓘ |
| develops |
adelic approach to algebraic groups
ⓘ
connections between adeles and arithmetic of algebraic groups ⓘ |
| field |
adelic theory
ⓘ
algebraic geometry ⓘ algebraic groups ⓘ number theory ⓘ |
| focusesOn |
adeles
ⓘ
algebraic groups ⓘ applications to number theory ⓘ |
| hasPart |
applications to arithmetic problems
ⓘ
structure of algebraic groups over global fields ⓘ theory of adeles ⓘ |
| hasReputation |
highly influential in modern number theory
ⓘ
technically demanding ⓘ |
| hasSubject |
adelic description of algebraic groups
ⓘ
adelic topologies on algebraic groups ⓘ arithmetic properties of algebraic groups over number fields ⓘ connections between local and global fields via adeles ⓘ measure-theoretic aspects of adeles ⓘ |
| influenced |
modern adelic methods in number theory
ⓘ
research on arithmetic of algebraic groups ⓘ |
| isConsidered |
classic text in the theory of algebraic groups
ⓘ
foundational work in adelic number theory ⓘ |
| isUsedIn |
advanced graduate study in number theory
ⓘ
research on arithmetic geometry ⓘ research on automorphic representations ⓘ |
| language | English ⓘ |
| relatedTo |
automorphic forms
ⓘ
class field theory ⓘ global fields ⓘ representation theory of algebraic groups ⓘ |
| usesConcept |
algebraic group schemes
ⓘ
ideles ⓘ rational points of algebraic groups ⓘ ring of adeles ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Adeles and Algebraic Groups Description of subject: "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Adeles and Algebraic Groups