Indian Institute of Technology, Bombay

Powai, Mumbai 400076 India

1 | Field Extensions | 2 |
---|---|---|

1.1 Basic Facts | 2 | |

1.2 Basic Examples | 5 | |

1.3 Cyclic Extensions | 8 | |

1.4 Abelian Extensions | 11 | |

1.5 Discriminant | 13 | |

2 | Ramification Theory | 20 |

2.1 Extensions of Primes | 21 | |

2.2 Kummer's Theorem | 24 | |

2.3 Dedekind's Discriminant Theorem | 25 | |

2.4 Ramification in Galois Extensions | 37 | |

2.5 Decomposition and Inertia Groups | 29 | |

2.6 Quadratic and Cyclotomic Extensions | 31 | |

Bibliography | 35 | |

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