Meeting times: MWF, 2-2:50pm in Room 12 of MSB.
email: firstname.lastname@youknowwhat.edu
Office Hours: By appointment or Wednesdays from 3-4pm and Fridays from 3-4pm.
This is a second course in commutative algebra. We will first finish discussing some topics we did not get to last semester, such as completions. We will develop the theory of completions as generally as possible, without delving into the topic of derived completions. We will then prove some more advanced results on universal injectivity and flatness. We will then introduce the module of Kahler differentials, introduce the notion of separability of an algebra (generalizing the usual definition of separable field extensions) and undertake a differential study of ring homomorphisms, covering topics such as unramified, smooth and etale homomorphisms.
Grades:
These will be based on attendance and class participation. I might also require each of you to do a final presentation. There will be frequent exercises and questions raised (often in red) within the notes. The best way to learn is to attempt all the problems and questions, although I am not requiring you to submit them.
Course notes:
They will be posted here.
References:
There are no required texts for this course. However, here are some resources:
Notes by Melvin Hochster on similar topics.
The Stacks Project chapters 10, 15, 16.
The first chapter of the book Néron Models.