| 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 (Sn) |
| 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 |