object of arithmetic geometry
C59704
concept
An object of arithmetic geometry is a mathematical structure, such as a scheme or variety, studied simultaneously with its geometric properties and its arithmetic behavior over number-theoretic base rings or fields.
All labels observed (3)
| Label | Occurrences |
|---|---|
| theory in arithmetic geometry | 3 |
| generalization of elliptic curves | 1 |
| object of arithmetic geometry canonical | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: object of arithmetic geometry
Generated description
An object of arithmetic geometry is a mathematical structure, such as a scheme or variety, studied simultaneously with its geometric properties and its arithmetic behavior over number-theoretic base rings or fields.
Instances (5)
| Instance | Via concept surface |
|---|---|
| Arakelov theory | theory in arithmetic geometry |
| Shimura varieties | — |
| Drinfeld modules | generalization of elliptic curves |
| Tate’s non-archimedean uniformization of elliptic curves | theory in arithmetic geometry |
| Bruhat–Tits theory | theory in arithmetic geometry |