Global Fields#

Number Fields

Defining number fields, elements and embeddings.

Number Fields
Quadratic Fields

Quadratic field creation, structure and element operations.

Quadratic Fields
Cyclotomic Fields

Cyclotomic field creation, structure and element operations.

Cyclotomic Fields
Number Fields and Orders

Orders in number fields: creation, arithmetic and printing.

Number Fields and Orders
Galois Groups and Automorphisms

Automorphism groups, Galois groups, subfields and cohomology.

Galois Groups and Automorphisms
Class Field Theory

Abelian extensions, ray class fields and Galois module structure.

Class Field Theory
Étale Algebras

Étale algebra construction, attributes and homomorphisms.

Étale Algebras
Dirichlet and Hecke Characters

Dirichlet and Hecke character construction and properties.

Dirichlet and Hecke Characters
Algebraically Closed Fields

Algebraically closed field representation, structure and creation.

Algebraically Closed Fields
Rational Function Fields

Rational function field creation, operations and elements.

Rational Function Fields
Algebraic Function Fields

Algebraic function field creation and structural invariants.

Algebraic Function Fields
Class Field Theory for Global Function Fields

Class groups, abelian extensions and Witt rings for function fields.

Class Field Theory for Global Function Fields
Artin Representations

Artin representation functions, invariants and arithmetic.

Artin Representations