Course : Math 996, Topics in Commutative Algebra. In this course we will discuss a set of problems that are collectively known as the `homological conjectures' in commutative algebra. Roughly speaking, these questions arose during the late 1960's and early 1970's in the work of Peskine-Szpiro, M. Hochster, Paul Roberts and others, and have their origins in intersection theory and invariant theory. Many of these conjectures are valid for local rings containing a field, and one of the goals of the course is to present proofs in these cases. The proofs of these results will rely heavily on the technique of combining Artin approximation with reduction to positive characteristic. These latter topics were covered in Math 996 last fall by Craig Huneke. As time permits, we will look at what's known in the case of mixed characteristic, i.e., the case of local rings not containing a field.
Time and Place : TR, 1:00-2:15, Snow 456
Instructor : D. Katz
Office : Snow 501
Office hours : MWF 1:00-2:00 and by appointment
Grading : Every student enrolled in the class will be required to take the final exam. The final exam will be an in-class exam that tests concepts covered in the course. In particular, you will be required to state definitions and theorems covered during the semester and answer very brief questions about them.
Final Exam date : Monday, May 12, 1:30pm - 4:00pm
Text : No text is required.