Module

IdeleClassFormation.lean

Nyll.ClassFieldTheory.GlobalClassFieldTheory.ClassFieldAxiom.IdeleClassFormation
1 declaration indexed from sourceView source ↗

The rational idele-class formation

This module identifies the fixed-field idele-class representation with concrete relative idele class groups and transfers the cyclic low-degree Tate cohomology calculation to prove the abstract class-field axiom.

Declarations

GlobalClassFieldTheory.Reciprocity.rationalIdeleClassRepresentation_satisfiesClassFieldAxiom

The rational absolute idele-class representation satisfies the abstract class-field axiom.

Source context 8 commands

Surrounding namespaces, section variables, and local commands at this declaration.

namespace GlobalClassFieldTheory
open scoped NumberField TensorProduct
open NumberField
open CyclicCohomology ClassFormation
open LocalClassFieldTheory
noncomputable section
open CategoryTheory
namespace Reciprocity
theorem rationalIdeleClassRepresentation_satisfiesClassFieldAxiom :
    SatisfiesClassFieldAxiom rationalIdeleClassRepresentation