- Lecture times and location: MWF 9:55AM - 10:45AM, Van Vleck B305
- Textbook: David Eisenbud,
*Commutative Algebra: with a view toward algebraic geometry* - Course website: http://math.wisc.edu/~svs/746/
- Instructor: Steven Sam email
- Instructor office hours: 321 Van Vleck, Mondays 12-1 (shared with 742), Fridays 11-12
- Grader: Eric Ramos
- Course info: link
- Piazza page: link

- Homework 1 (due Feb 12): Eisenbud 10.12, 17.11, 17.21; comments on 17.21
- Homework 2 (tex file) - due Feb. 26
- Homework 3 (tex file) - due Mar. 18
- Homework 4 (tex file) - due Apr. 11

- Srikanth Iyengar et. al,
*Twenty-Four Hours of Local Cohomology* - Appendix 1 of David Eisenbud,
*The Geometry of Syzygies*

Jan 20 | Chapter 8: Summary of dimension theory |

Jan 22 | Section 10.0: Principal ideal theorem Section 10.1: Systems of parameters |

Jan 25 | Section 17.1: Koszul complexes of lengths 1 and 2 |

Jan 27 | Section 17.2: Koszul complexes in general |

Jan 29 | Section 17.3: Building the Koszul complex from parts |

Feb 1 | Finish 17.3 |

Feb 3 | Guest lecture: Arinkin |

Feb 5 | Guest lecture: Arinkin |

Feb 8 | Section 18.1: Depth |

Feb 10 | Section 18.2: Cohen-Macaulay rings |

Feb 12 | Finish 18.2 |

Feb 15 | Section 16.6: Jacobian criteria for regularity Section 18.3: Serre's conditions (S _{n}) |

Feb 17 | Section 18.4: Flatness and depth Section 18.5: Examples |

Feb 19 | Section 19.1: Projective dimension and minimal resolutions Section 19.2: Hilbert syzygy theorem |

Feb 22 | Section 19.3: Auslander-Buchsbaum formula |

Feb 24 | Section 19.4: Stably free modules and factoriality of regular local rings |

Feb 26 | Section 20.1: Uniqueness of free resolutions |

Feb 29 | Section 20.2: Fitting ideals |

Mar 2 | Section 20.3: What makes a complex exact? |

Mar 4 | Section 20.4: Hilbert-Burch theorem |

Mar 7 | Section 20.5: Castelnuovo-Mumford regularity |

Mar 9 | Section 15.1, 15.2: Monomials and monomial orderings |

Mar 11 | Section 15.8: Gröbner bases and flat families |

Mar 14 | Section 15.9: Generic initial ideals |

Mar 16 | Section 15.3, 15.4: Division algorithm, Buchberger's criterion |

Mar 18 | Section 15.5: Schreyer's theorem |

Spring break | |

Mar 28 | Local cohomology: definitions, Čech complex |

Mar 30 | Local duality (polynomial rings) |

Apr 1 | Mayer-Vietoris sequence, Local cohomology and depth, sheaf cohomology |

Apr 4 | no class |

Apr 6 | no class |

Apr 8 | no class |

Apr 11 | Local cohomology and Hilbert polynomials, regularity |

Apr 13 | 24, Appendix, Section 11.1: Injective modules, Bass numbers |

Apr 15 | 24, Section 11.2: Gorenstein rings |

Apr 18 | 24, Section 11.4: Local duality (Gorenstein rings) |

Apr 20 | 24, Section 11.5: Canonical modules |

Apr 22 | Canonical modules continued |

Apr 25 | Local and sheaf cohomology |

Apr 27 | 24, Chapter 9: Cohomological dimension |

Apr 29 | 24, Section 15.2: Connectedness theorems of Faltings, Fulton-Hansen |

May 2 | Finish 15.2 |

May 4 | Eagon-Northcott complex |

May 6 | Kempf collapsing, see notes |