---
date: 2022-01-26 08:59
modification date: Wednesday 26th January 2022 08:59:18
title: 020 Defiinitions
aliases: [020 Defiinitions]
---

Tags: 
#todo #NT/algebraic 
Refs:
?

# Defiinitions

- [absolute Galois group](Unsorted/absolute%20Galois%20group.md)
- [Eisenstein polynomial](Eisenstein%20polynomial)
- [different](different) and [discriminants](Unsorted/discriminants.md)
- [field norm](Unsorted/field%20norm.md) and [trace](Unsorted/field%20norm.md)
- [cyclotomic character](cyclotomic%20character)
- [maximal unramified extension](maximal%20unramified%20extension)
- [maximal abelian extension](maximal%20abelian%20extension.md)
- [Haar measure](Haar%20measure)
- What is the [degree of a number field](degree%20of%20a%20number%20field)?
- What is a rational prime?
- What is the [Artin symbol](Artin%20symbol.md)?
- What is the [Norm-residue symbol](Norm-residue%20symbol)?
- What are the [Ideles](Unsorted/Ideles.md)?
- What are the [Adeles](Adeles)?
- What is the [trace pairing](trace%20pairing.md)?
	- [different](Unsorted/different.md) and [discriminants](Unsorted/discriminants.md); basic properties of [local fields](Unsorted/global%20field.md).
- What is an [Arakelov](Unsorted/Arakelov.md)?
- What is the [regulator](regulator) of a number field?
- What is a [Pell equation](Pell%20equation.md)?
- What is a [ray class field](ray%20class%20field.md)?
- What are [coinvariants](Unsorted/coinvariants.md) and invariants?
- What is the [norm group](norm%20group.md)?

# Notation
![](attachments/Pasted%20image%2020220202230347.png)
![](attachments/Pasted%20image%2020220126164200.png)