Local Fields
E253119
"Local Fields" is a foundational mathematical text by Jean-Pierre Serre that develops the theory of local fields and their applications in number theory and algebraic geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Local Fields canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T2306398 — 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: Local Fields Context triple: [Jean-Pierre Serre, notableWork, Local Fields]
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A.
Regions Field
Regions Field is a modern minor league baseball stadium in Birmingham, Alabama, serving as the home of the Birmingham Barons.
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B.
Field
Field is a common English surname borne by numerous notable individuals across business, politics, sports, and the arts.
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C.
Fields
Fields is a common English surname borne by numerous notable individuals across diverse fields such as entertainment, sports, and academia.
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D.
Flatlands
Flatlands is a residential neighborhood in southeastern Brooklyn, New York City, known for its low-rise housing, suburban feel, and diverse community.
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E.
Localish
Localish is a lifestyle-focused digital media brand and programming initiative that produces short-form, feel-good stories about local communities, food, and culture across the United States.
- 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: Local Fields Target entity description: "Local Fields" is a foundational mathematical text by Jean-Pierre Serre that develops the theory of local fields and their applications in number theory and algebraic geometry.
-
A.
Regions Field
Regions Field is a modern minor league baseball stadium in Birmingham, Alabama, serving as the home of the Birmingham Barons.
-
B.
Field
Field is a common English surname borne by numerous notable individuals across business, politics, sports, and the arts.
-
C.
Fields
Fields is a common English surname borne by numerous notable individuals across diverse fields such as entertainment, sports, and academia.
-
D.
Flatlands
Flatlands is a residential neighborhood in southeastern Brooklyn, New York City, known for its low-rise housing, suburban feel, and diverse community.
-
E.
Localish
Localish is a lifestyle-focused digital media brand and programming initiative that produces short-form, feel-good stories about local communities, food, and culture across the United States.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematician
ⓘ
mathematics book ⓘ monograph ⓘ |
| author | Jean-Pierre Serre ⓘ |
| authorInstanceOf | Jean-Pierre Serre ⓘ |
| field |
algebra
ⓘ
algebraic geometry ⓘ number theory ⓘ |
| hasPart |
Witt vector constructions
ⓘ
applications to curves over local fields ⓘ local class field theory ⓘ ramification and different ⓘ structure of unramified extensions ⓘ theory of complete discrete valuation fields ⓘ |
| influenced |
modern local class field theory expositions
ⓘ
research in p-adic number theory ⓘ |
| languageOfAvailableTranslation | English ⓘ |
| notableFor |
clear development of ramification theory
ⓘ
concise and rigorous exposition ⓘ influence on modern arithmetic geometry ⓘ systematic treatment of local fields ⓘ |
| originalLanguage | French ⓘ |
| originalTitle | Corps locaux ⓘ |
| subjectOf |
graduate reading courses in number theory
ⓘ
research seminars in arithmetic geometry ⓘ |
| title | Local Fields self-link ⓘ |
| topic |
Galois theory of local fields
ⓘ
Henselian fields ⓘ Witt vectors ⓘ applications to algebraic geometry ⓘ applications to number theory ⓘ complete discrete valuation rings ⓘ discrete valuation fields ⓘ higher ramification groups ⓘ local class field theory ⓘ local fields ⓘ local zeta functions ⓘ p-adic fields ⓘ ramification theory ⓘ ramified extensions ⓘ residue fields ⓘ unramified extensions ⓘ valuation theory ⓘ |
| usedAs | graduate-level textbook ⓘ |
| usedIn |
advanced number theory courses
ⓘ
algebraic geometry seminars ⓘ |
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: Local Fields Description of subject: "Local Fields" is a foundational mathematical text by Jean-Pierre Serre that develops the theory of local fields and their applications in number theory and algebraic geometry.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.