Tuesday | Thursday |
---|---|

Aug. 28
In Lecture: - Overview of the course
- Beginning of classical Iwasawa theory
Associated Reading: - Chapters 1 - 5 of Washington's book
Video of class (downloadable) | Aug. 30
In Lecture: - Class field theory
- Classical Iwasawa theory, continued
Associated Reading: - Appendix 3 of Washington's book
- Chapters 1 - 5 of Washington's book
Video of class (downloadable) |

Sept. 4
In Lecture: - Leopoldt's conjecture and its relation to Z_p extensions of number fields
- The conjectures of Iwasawa and Greenberg on the psuedonullity of certain Galois groups.
Associated Reading: - Chapters 13 of Washington's book
Video of class (downloadable) | Sept. 6
In Lecture: - Structure theory for Z_p[[Z_p]] modules
- Vandiver's conjecture
Associated Reading: - Chapters 13 and 15 of Washington's book
Video of class (downloadable) |

Sept. 11
In Lecture: - Statement of the classical main conjecture
- The Herbrand-Ribet Theorem
Associated Reading: - Chapters 13 of Washington's book
Video of class (downloadable) | Sept. 13
In Lecture: - The Herbrand-Ribet Theorem, continued
- Iwasawa modules with no finite submodules
Associated Reading: - Chapters 8, 13 and 15 of Washington's book
Video of class (downloadable) |

Sept. 18
In Lecture: - Iwasawa modules with no finite submodules (continued)
- Stickleberger's theorem
Associated Reading: - Chapters 13 of Washington's book
Video of class (downloadable) | Sept. 20
In Lecture: - Arithmetic topology
- Gauss sums
- Stickleberger's Theorem, continued
Associated Reading: - Chapters 8, 13 and 15 of Washington's book
Video of class (downloadable) |

Sept. 25
In Lecture: - p-adic representations of groups
- Continuous group cohomology
- Hochschild-Serre Spectral sequence
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) | Sept. 27
In Lecture: - Low degree exact sequences arising from spectral sequences
- Cohomology of modules for cyclic and pro-cyclic groups
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) |

Oct. 2
In Lecture: - pro-finite cohomology of modules for the profinite completion of Z.
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) | Oct. 4
No class - Fall Break. |

Oct. 9
In Lecture: - Selmer groups
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) | Oct. 11
In Lecture: - local and global duaiity
- Euler systems
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) - to be posted |

Oct. 9
In Lecture: - Selmer groups
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) | Oct. 11
In Lecture: - local and global duaiity
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) |

Oct. 16
In Lecture: - global duality, continued
- Euler systems
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) - to be posted | Oct. 18
In Lecture: - Euler systems, continued
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) |

Oct. 23
In Lecture: - The cyclotomic Euler system
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) | Oct. 25
In Lecture: - Kolyvagin derivatives
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) |

Oct. 30
In Lecture: - Kolyvagin derivatives, continued
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) | Nov. 1
In Lecture: - Local properties of Kolyvagin derivatives at primes not dividing the level
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) |

Nov. 6
In Lecture: - Local properties of Kolyvagin derivatives at primes dividing the level
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) | Nov. 8
In Lecture: - Statement of bounds on Selmer groups, classical applications
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) |

Nov. 13
In Lecture: - Sketch of the proof of bounds on Selmer groups in terms of Selmer groups
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) | Nov. 15
In Lecture: - Bounding Selmer groups, continued
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) |

Nov. 20
In Lecture: - End of Euler systems
Associated Reading: - The relevant parts of Rubin's "Euler systems"
Video of class (downloadable) | Nov. 22
No class - Thanksgiving Break! |

Nov. 27
In Lecture: - Ribet's proof of the converse of the Herbrand criterion
Associated Reading: Video of class (downloadable) | Nov. 29
In Lecture: - Ribet's proof, continued
Associated Reading: Video of class (downloadable) - to be posted |

Dec. 4
In Lecture: - Ribet's proof, continued
Associated Reading: Video of class (downloadable) | Dec. 6
In Lecture: - Ribet's proof, continued
Associated Reading: Video of class (downloadable) |

Last updated: 11/22/18

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