Math 245: Stacks

 Winter 2017

Tuesdays and Thursdays 10:30-11:50 in 381-T

The goal of this class is to gain familiarity and comfort with algebraic spaces and stacks, largely following Martin Olsson's excellent book. I will try to keep things motivated, technically complete and concrete.

Prerequisites. Comfort with algebraic geometry (the language of schemes), combined with a willingness to work with things you haven't fully mastered.

  • Martin Olsson's graduate level textbook on Algebraic spaces and stacks.
  • What is a stack?, by Dan Edidin.
  • Equivariant geometry and the cohomology of the moduli space of curves, by Dan Edidin.
  • Notes on the construction of the moduli space of curves, by Dan Edidin.
  • Stacks for Everybody, by Barbara Fantechi.
  • Picard groups of moduli problems, by David Mumford, and Daniel Litt's exposition thereof (parts one and two).
  • Notes on Grothendieck topologies, fibered categories and descent theory, by Angelo Vistoli (lovely comprehensive reference).

    • Course email list. Please be sure you are on the course email list (by asking me).

    Instructor: Ravi Vakil (office 383-Q, office hours TBA, but possibly just by appointment if I know everyone in the class well enough).

    The notes for this class are here. Tony Feng, Dan Dore, and Aaron Landesman very very kindly livetexed the classes. The link to edit the notes is in the January 15 email sent to our class email list.

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