Algebraic Geometry Graduate Reading Course

[math]\displaystyle{ \operatorname{Hom}_{\rm Schemes}(X, \operatorname{Spec}(A)) \cong \operatorname{Hom}_{\rm CRing}(A, {\mathcal O}_X(X)). }[/math]

Schedule

M: 3:30-5:00, With faculty W: 3:30-4:30 F: 7:45-8:50

Location: TBA

Structure of Course

Our reading group will meet three times a week. A new discussion leader will lead our meetings each Wednesday, Friday, and Monday. The monday meetings will culminate with a visit from Jordan, David or Andrei to answer that section's questions, provide feedback, and so on.

Homework

Doing exercises is very important in mastering this material. Ravi's notes contain many, many exercises. You should hand in 6 written up exercises each Wednesday, starting September 8th.

We'll collect homework at our meeting, and distribute it to the grader. In fairness to our grader, no late homework will be accepted.

Responsibilities of Discusssion Leaders

Discussion leaders are responsible for leading a full week of seminars. In the previous week DL's should:

1. Check Ravi's blog. Remeber that notes are posted every two weeks. Get a feel for what we are discussing. A new set of notes? Finishing the previous set?
2. Get comfortable with editing the wiki. We aim to have a page devoted for each chapter in Ravi's notes. The discussion leader is responsible for posting any comments, questions, and other thoughts in the wiki. Ask Lalit or David for help.
3. Decide which sections we should read by which days. Note: We want to cover all sections that Ravi recommends. For example, if he says skip 2.7 Spectral Sequences, we should. Otherwise nothing should be left out. Email this information by the Friday the week before but no later.

The week of:

1. Be ready to lead the class in a discussion of the material. How you want this to look is up to you. It is not necessary to lecture, and do not feel the need to present the material (everybody should have read the same thing you have read). This does not mean you should skip over sections, instead discuss the nuances in the notes and the big picture ideas. For example, you can discuss problems, or ask/answer clarifying questions.
2. Make an effort to include everyone in the discussion. What is easy for you may not be easy for everyone. You might have learned tensor products in 3rd grade but not all of us know what it is.
3. Every day we meet, keep a list of what we thought was easy, tricky and what specific questions we have. This will form a starting point for what we want to discuss with faculty.
4. After each meeting post the previous to the wiki.
5. Very important: On Friday email our faculty sponsors with the list of questions/thoughts/ruminations from the week. The faculty need this information on Friday, so that the following Monday they're prepared to meet with us.