I will keep a schedule of what I hope to cover in the seminar on this page. I will also post some useful resources. This is Not designed to be an introductory course/seminar and I will be assuming a first course in commutative and homological algebra. I have notes on my webpage here that constitute the prerequisites I am assuming. If you see something you don't recognize, you might be able to find an answer here.

I will be adding to these notes as we go, starting with depth. My goal is to eventually talk about local cohomology and some of the interesting open problems regarding it. I'll update this as we go along.

Depth Notes

Injective Modules Notes

Local Cohomology Notes Applications and Generalizations Notes

Date | Topic |

9/29 | Depth and Vanishing of Ext |

10/6 | Koszul Complex and Free Resolutions |

10/13 | Cohen-Macaulay Rings and Modules |

10/20 | Hartshorne's Connectedness Theorem and Injective Envelopes |

10/27 | Matlis Duality |

11/3 | Minimal Injective Resolutions |

11/10 | Gorenstein Rings |

11/17 | 4 Definitions of Local Cohomology |

11/24 | No Seminar - Thanksgiving |

12/1 | Local Duality |

1/19 | Hartshorne-Lichtenbaum Vanishing Theorem |

1/26 | Falting's Connectedness Theorem |

2/2 | Infinite Free Resolutions - Ines takes over |