Stack Learning Seminar

• Sep 6th

• Sep 13th

• Sep 20th

• Sep 27th

• Oct 4th

• Oct 11th

• Oct 18th

• Oct 25th

• Nov 1st

• Nov 22nd (by Tingting)

Topics: Introducing moduli problems, functorial viewpoint, and representability of functors. Motivates the definition of stacks.

Topics: Grothendieck topology, sites, and sheaves.

Topics: Groupoids and prestacks.

Topics: A brief discourse on descent before introducing stacks.

Topics: Introduce definitions of algebraic spaces and algebraic stacks. Representability of the diagonal and stabilizers.

Topics: Examples of algebraic stacks, properties of (morphisms of) algebraic stacks, and topological spaces of stacks. 

Topics: Dimension and tangent space of algebraic stacks. Introduce residual gerbe at a point.

Topics: Miniversal presentation of algebraic stack via residual gerbes. Infinitesimal lifting property of smoothness.

Topics: Introduce quasi-coherent sheaves on Deligne-Mumford stacks. Investigate one specific example: for a finite group G over a field k, QCoh(BG) = Rep(G).

Speaker is away.

Speaker is away.

Topics: Coarse moduli space, geometric quotients, and local structure of DM stacks. Setting up ingredients towards Keel-Mori Theorem.

Due to Thanksgiving break.

Topics: Sketch the proof of Keel-Mori Theorem and illustrate some examples, consequences, and generalizations.