result in local class field theory
C24994
concept
The "result" in local class field theory refers to the fundamental correspondence that classifies finite abelian extensions of a local field in terms of open subgroups of finite index in its multiplicative group (or, equivalently, its Galois group via the local reciprocity map).
All labels observed (3)
| Label | Occurrences |
|---|---|
| result in class field theory | 2 |
| result in local class field theory canonical | 1 |
| tool in local class field theory | 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: result in local class field theory
Generated description
The "result" in local class field theory refers to the fundamental correspondence that classifies finite abelian extensions of a local field in terms of open subgroups of finite index in its multiplicative group (or, equivalently, its Galois group via the local reciprocity map).
Instances (4)
| Instance | Via concept surface |
|---|---|
| Hasse–Arf theorem | — |
| Artin reciprocity law | result in class field theory |
| Furtwängler’s theorem in class field theory | result in class field theory |
| Herbrand function | tool in local class field theory |