Algebraic Groups and Class Fields
E325282
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Algebraic Groups and Class Fields canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3072660 — 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: Algebraic Groups and Class Fields Context triple: [Annals of Mathematics Studies, hasNotableWork, Algebraic Groups and Class Fields]
-
A.
Adeles and Algebraic Groups
"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.
-
B.
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.
-
C.
Deligne–Lusztig theory
Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
-
D.
A Course in Arithmetic
A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
-
E.
Cohomologie Galoisienne
Cohomologie Galoisienne is a foundational monograph by Jean-Pierre Serre that systematically develops Galois cohomology and its deep applications in number theory and algebraic geometry.
- 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: Algebraic Groups and Class Fields Target entity description: "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
-
A.
Adeles and Algebraic Groups
"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.
-
B.
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.
-
C.
Deligne–Lusztig theory
Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
-
D.
A Course in Arithmetic
A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
-
E.
Cohomologie Galoisienne
Cohomologie Galoisienne is a foundational monograph by Jean-Pierre Serre that systematically develops Galois cohomology and its deep applications in number theory and algebraic geometry.
- F. None of above. chosen
Statements (33)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ research monograph ⓘ |
| contribution |
develops connections between algebraic group theory and class field theory
ⓘ
influences research in number theory and arithmetic geometry ⓘ |
| field |
algebraic geometry
ⓘ
algebraic group theory ⓘ arithmetic geometry ⓘ class field theory ⓘ mathematics ⓘ number theory ⓘ |
| genre | advanced mathematics text ⓘ |
| hasDiscipline | pure mathematics ⓘ |
| hasPerspective | research-level exposition ⓘ |
| hasSubjectArea |
Galois theory
ⓘ
abelian extensions of number fields ⓘ arithmetic of field extensions ⓘ cohomological methods in number theory ⓘ global fields ⓘ local fields ⓘ structure of algebraic groups ⓘ |
| intendedAudience |
graduate students in mathematics
ⓘ
research mathematicians ⓘ |
| isAbout |
applications of algebraic groups to number theory
ⓘ
applications of class field theory to algebraic groups ⓘ relationships between algebraic groups and class field theory ⓘ |
| language | English ⓘ |
| topic |
Galois representations
ⓘ
algebraic groups ⓘ arithmetic of algebraic groups ⓘ class fields ⓘ connections between algebraic groups and class field theory ⓘ |
| workType | theoretical ⓘ |
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: Algebraic Groups and Class Fields Description of subject: "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.