Triple

T17671630
Position Surface form Disambiguated ID Type / Status
Subject Goro Shimura E440532 entity
Predicate notableWork P4 FINISHED
Object Abelian Varieties with Complex Multiplication and Modular Functions
"Abelian Varieties with Complex Multiplication and Modular Functions" is a foundational monograph by Goro Shimura that develops the arithmetic theory of abelian varieties with complex multiplication and their deep connections to modular and automorphic functions.
E1281168 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Abelian Varieties with Complex Multiplication and Modular Functions | Statement: [Goro Shimura, notableWork, Abelian Varieties with Complex Multiplication and Modular Functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Abelian Varieties with Complex Multiplication and Modular Functions
Context triple: [Goro Shimura, notableWork, Abelian Varieties with Complex Multiplication and Modular Functions]
  • A. Shimura varieties
    Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
  • B. Baker’s theory of Abelian functions
    Baker’s theory of Abelian functions is a foundational mathematical work that systematically develops the theory of Abelian functions and their applications in complex analysis and algebraic geometry.
  • C. Introduction to Elliptic Curves and Modular Forms
    Introduction to Elliptic Curves and Modular Forms is a graduate-level mathematics textbook that develops the theory of elliptic curves and their deep connections to modular forms, number theory, and arithmetic geometry.
  • D. Drinfeld modules
    Drinfeld modules are algebraic structures that generalize elliptic curves to the setting of function fields, playing a central role in modern arithmetic geometry and the theory of automorphic forms.
  • E. Jacobian varieties
    Jacobian varieties are complex algebraic varieties associated to algebraic curves that parametrize degree-zero line bundles (or divisor classes) on the curve and carry a natural structure of principally polarized abelian varieties.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Abelian Varieties with Complex Multiplication and Modular Functions
Triple: [Goro Shimura, notableWork, Abelian Varieties with Complex Multiplication and Modular Functions]
Generated description
"Abelian Varieties with Complex Multiplication and Modular Functions" is a foundational monograph by Goro Shimura that develops the arithmetic theory of abelian varieties with complex multiplication and their deep connections to modular and automorphic functions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Abelian Varieties with Complex Multiplication and Modular Functions
Target entity description: "Abelian Varieties with Complex Multiplication and Modular Functions" is a foundational monograph by Goro Shimura that develops the arithmetic theory of abelian varieties with complex multiplication and their deep connections to modular and automorphic functions.
  • A. Shimura varieties
    Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
  • B. Baker’s theory of Abelian functions
    Baker’s theory of Abelian functions is a foundational mathematical work that systematically develops the theory of Abelian functions and their applications in complex analysis and algebraic geometry.
  • C. Introduction to Elliptic Curves and Modular Forms
    Introduction to Elliptic Curves and Modular Forms is a graduate-level mathematics textbook that develops the theory of elliptic curves and their deep connections to modular forms, number theory, and arithmetic geometry.
  • D. Drinfeld modules
    Drinfeld modules are algebraic structures that generalize elliptic curves to the setting of function fields, playing a central role in modern arithmetic geometry and the theory of automorphic forms.
  • E. Jacobian varieties
    Jacobian varieties are complex algebraic varieties associated to algebraic curves that parametrize degree-zero line bundles (or divisor classes) on the curve and carry a natural structure of principally polarized abelian varieties.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d8b9e87e18819087104a44dc4dc5b1 completed April 10, 2026, 8:50 a.m.
NER Named-entity recognition batch_69e46f69b11c8190b09add33f81776b3 completed April 19, 2026, 6 a.m.
NED1 Entity disambiguation (via context triple) batch_6a02166234f0819099c452808234e3e4 completed May 11, 2026, 5:48 p.m.
NEDg Description generation batch_6a0217ca2ec881908573b0423c3610f7 completed May 11, 2026, 5:54 p.m.
NED2 Entity disambiguation (via description) batch_6a0218636e048190a48bc7f066c7bee1 completed May 11, 2026, 5:56 p.m.
Created at: April 10, 2026, 9:59 a.m.