Introduction to the Theory of Algebraic Functions of One Variable
E559866
Introduction to the Theory of Algebraic Functions of One Variable is a classic monograph by Claude Chevalley that provides a rigorous, modern foundation for the theory of algebraic function fields in one variable.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Introduction to the Theory of Algebraic Functions of One Variable canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5970309 — 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: Introduction to the Theory of Algebraic Functions of One Variable Context triple: [Claude Chevalley, notableWork, Introduction to the Theory of Algebraic Functions of One Variable]
-
A.
Theorie der algebraischen Kurven
"Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
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B.
Sur les courbes algébriques et les variétés qui s’en déduisent
Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
-
C.
Theorie der algebraischen Zahlen
"Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
-
D.
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.
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E.
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.
- 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: Introduction to the Theory of Algebraic Functions of One Variable Target entity description: Introduction to the Theory of Algebraic Functions of One Variable is a classic monograph by Claude Chevalley that provides a rigorous, modern foundation for the theory of algebraic function fields in one variable.
-
A.
Theorie der algebraischen Kurven
"Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
-
B.
Sur les courbes algébriques et les variétés qui s’en déduisent
Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
-
C.
Theorie der algebraischen Zahlen
"Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (38)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics monograph ⓘ |
| approach |
axiomatic
ⓘ
modern algebraic ⓘ rigorous ⓘ |
| author | Claude Chevalley ⓘ |
| authorNationality | French ⓘ |
| emphasis |
Riemann–Roch spaces
ⓘ
linked to:
Riemann–Roch theorem
divisor theory ⓘ structure of places and valuations ⓘ |
| field | mathematics ⓘ |
| focus | function fields of one variable over a field ⓘ |
| hasReputation |
classic text in algebraic geometry
ⓘ
standard reference on algebraic function fields ⓘ |
| influenced |
modern treatments of algebraic curves
ⓘ
subsequent textbooks on algebraic function fields ⓘ |
| intendedAudience |
graduate students in mathematics
ⓘ
research mathematicians ⓘ |
| language | English ⓘ |
| mathematicalArea |
theory of algebraic curves over fields
ⓘ
theory of algebraic functions ⓘ |
| relatedTo |
Weil’s foundations of algebraic geometry
ⓘ
linked to:
Grothendieck’s scheme-theoretic framework
class field theory of function fields ⓘ |
| subfield |
algebra
ⓘ
algebraic geometry ⓘ number theory ⓘ |
| topic |
Riemann–Roch theorem
ⓘ
algebraic curves ⓘ algebraic function fields in one variable ⓘ differentials on curves ⓘ divisors ⓘ extensions of function fields ⓘ genus of a function field ⓘ places of function fields ⓘ ramification theory ⓘ valuations ⓘ |
| usedIn |
graduate courses on algebraic curves
ⓘ
graduate courses on algebraic function fields ⓘ |
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: Introduction to the Theory of Algebraic Functions of One Variable Description of subject: Introduction to the Theory of Algebraic Functions of One Variable is a classic monograph by Claude Chevalley that provides a rigorous, modern foundation for the theory of algebraic function fields in one variable.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
Claude Chevalley
→
notableWork
→
Introduction to the Theory of Algebraic Functions of One Variable
ⓘ