Main Page/Reading Seminar Stacks (2025)

Logistics: TBD

Tentative schedule

date	speaker	title	topics
	Hairuo	Grothendieck Topologies / Sites	Introduction to Grothendieck Toplogies /sites. More information can be found in Notes on a Seminar by Michael Artin. If one wishes to presert more on the \'etale site, Milne's Lecture Notes has far more details.
		Fibred Categories	Introduction to fibred categories. Describe correspondence between fibred categories /C and presheaves on C. Groupoids in C, fibre products of fibred categories, Yoneda Lemma, and discussion of categories fibred in groupoids. Discuss examples. The following exercises in Olsson are relevant for the future: 3.A, 3.B, 3.C, 3.D, 3.F, and 3.G.
		Descent and Stack Conditions
		Algebraic Spaces Part 1
		Algebraic Spaces Part 2
		Algebraic Spaces Part 3
		Algebraic Stacks
		Expedition: Quot Scheme and Hilbert Scheme
		Quasicoherent Sheaves on Algebraic Stacks
		Coarse Moduli Spaces and Moduli of Curves
		Gerbes
		Local Structure of Algebraic Stacks
		Coarse Moduli Spaces and Geometric Invariant Theory
Future Potential Topics		Bun_G (perhaps following Sorger), Artin Algebraization, Formal Moduli, etc. We'll figure it out when we get there.

References

1. Martin Olsson's Algebraic Spaces and Stacks
2. Laumon-Moret-Bailly Champs Algebriques
3. Alper's Stacks and Moduli