Neukirch: Algebraic Number Theory
E459564
"Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Neukirch: Algebraic Number Theory canonical | 2 |
| Algebraic Number Theory | 1 |
| Neukirch: Algebraische Zahlentheorie | 1 |
| Neukirch: Cohomology of Number Fields | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4597225 — 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: Neukirch: Algebraic Number Theory Context triple: [Kronecker–Weber theorem, standardReference, Neukirch: Algebraic Number Theory]
-
A.
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.
-
B.
Die Theorie der algebraischen Zahlkörper
"Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
-
C.
Algebraic Groups and Class Fields
"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.
-
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.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
- 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: Neukirch: Algebraic Number Theory Target entity description: "Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
-
A.
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.
-
B.
Die Theorie der algebraischen Zahlkörper
"Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
-
C.
Algebraic Groups and Class Fields
"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.
-
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.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic number theory textbook
ⓘ
mathematics book ⓘ textbook ⓘ |
| author | Jürgen Neukirch ⓘ |
| countryOfPublication | Germany ⓘ |
| field | algebraic number theory ⓘ |
| hasCompanionVolume |
Neukirch: Cohomology of Number Fields
ⓘ
linked to:
Neukirch: Algebraic Number Theory
|
| language |
English
ⓘ
German ⓘ |
| level | graduate ⓘ |
| notableFor |
idele-theoretic approach to class field theory
ⓘ
rigorous and modern treatment of class field theory ⓘ systematic use of valuations and completions ⓘ |
| originalPublicationYear | 1992 ⓘ |
| prerequisite |
Galois theory
ⓘ
abstract algebra ⓘ commutative algebra ⓘ |
| publicationYear | 1999 ⓘ |
| publisher |
Springer-Verlag
ⓘ
linked to:
Springer
|
| series |
Grundlehren der mathematischen Wissenschaften
ⓘ
Springer Monographs in Mathematics ⓘ |
| subject |
Artin reciprocity
ⓘ
linked to:
Artin reciprocity law
Dedekind domains ⓘ
linked to:
Dedekind domain
Dirichlet unit theorem ⓘ Galois theory of number fields ⓘ Kronecker–Weber theorem ⓘ L-functions ⓘ Minkowski theory ⓘ adeles ⓘ cohomological methods in number theory ⓘ discriminants ⓘ global class field theory ⓘ ideal class groups ⓘ ideles ⓘ local class field theory ⓘ local fields ⓘ local-global principles ⓘ number fields ⓘ ramification theory ⓘ units in number fields ⓘ valuations ⓘ zeta functions of number fields ⓘ |
| translatedFrom |
Neukirch: Algebraische Zahlentheorie
ⓘ
linked to:
Neukirch: Algebraic Number Theory
|
| translator |
Kay Wingberg
ⓘ
Norbert Schappacher ⓘ |
| usedAs | graduate textbook ⓘ |
| usedIn | graduate courses in algebraic number theory ⓘ |
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: Neukirch: Algebraic Number Theory Description of subject: "Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Neukirch: Algebraic Number Theory
linked to: Neukirch: Algebraic Number Theory
linked to: Neukirch: Algebraic Number Theory