Tags: #todo #NT/algebraic Refs: ?

Defiinitions

• absolute Galois group
• Eisenstein polynomial
• different and discriminants
• field norm and trace
• cyclotomic character
• maximal unramified extension
• maximal abelian extension
• Haar measure
• What is the degree of a number field?
• What is a rational prime?
• What is the Artin symbol?
• What is the Norm-residue symbol?
• What are the Ideles?
• What are the Adeles?
• What is the trace pairing?
  • different and discriminants; basic properties of local fields.
• What is an Arakelov?
• What is the regulator of a number field?
• What is a Pell equation?
• What is a ray class field?
• What are coinvariants and invariants?
• What is the norm group?

Notation