Topic outline

  • General

    Teaching staff:

    Alexander Engström (Lectures on Thursdays and Fridays)
    Milo Orlich (Exercise sessions on Mondays) <milo.orlich@aalto.fi>

    Zoom link: https://aalto.zoom.us/j/67633885686

    The lectures will be on Zoom. 

    The exercise sessions will be held in room U5 (U147) and can be followed on Zoom at the same time. This might change later to a fully remote setting. Remember to wear a face mask if you wish to attend the exercise sessions in person.

    Zulip link: https://ms-e1143.zulip.cs.aalto.fi/join/983boszziv3w68ukx6vmj3kz/

    Zulip is like a forum where you can post public messages or write to the other users privately. Please use Zulip to ask questions and discuss the topics in the course, in case you cannot attend the events in person nor on Zoom.

    Exercises, examination and grading:

    Your final grade is determined by the results of your submitted exercises, and in exceptional cases an oral exam with the lecturer. On Thursday afternoon and Friday morning you will hear about some new material on the lectures. Start trying to solve your weekly exercises about it immediately! You will most likely run into some trouble and questions — that’s part of the process. On late Monday afternoon you should attend the exercise session and bring your questions. That session is a golden opportunity to get help in internalising the material. On Thursday at noon is the deadline to submit the exercise solutions on MyCourses. They should be written up properly in LaTeX, but you may include hand-drawn scanned figures to save time. Anything submitted late is void. You are encouraged to talk to each other about algebraic geometry, but the exercise solutions have to be completed individually. If the lecturer is not convinced about your contribution, there will be an oral exam to determine your grade. Here you can find the assignments and submit your solutions.

    Tentative Schedule:

    Week 37

    Monday 16-18: Requested extra session to refresh algebra and geometry.
    Thursday 14-16, Friday 8-10: Chapter 1. Preliminaries. Some category theory.

    Week 38

    Monday 16-18: Exercise session focused on Exercise set 1.
    Thursday 12: Deadline to hand in Exercise set 1.
    Thursday 14-16, Friday 8-10: Chapter 2. Preliminaries. Sheaves.

    Week 39

    Monday 16-18: Exercise session focused on Exercise set 2.
    Thursday 12: Deadline to hand in Exercise set 2.
    Thursday 14-16, Friday 8-10: Chapter 3. Schemes. Toward affine schemes: the underlying set, and topological space.

    Week 40

    Monday 16-18: Exercise session focused on Exercise set 3.
    Thursday 12: Deadline to hand in Exercise set 3.
    Thursday 14-16, Friday 8-10: Chapter 4. Schemes. The structure sheaf, and the definition of schemes in general.

    Week 41

    Monday 16-18: Exercise session focused on Exercise set 4.
    Thursday 12: Deadline to hand in Exercise set 4.
    Thursday 14-16, Friday 8-10: Chapter 5. Schemes. Some properties of schemes

    Week 42

    Monday 16-18: Exercise session focused on Exercise set 5.
    Thursday 12: Deadline to hand in Exercise set 5.
    Thursday 14-16, Friday 8-10: An outlook towards morphisms of schemes.


    NB: Students from the University of Helsinki are welcome!