Algebraic Stacks

UGA MATH 8830, Fall 2014. An introductory course in the theory of Descent, Algebraic Spaces and Algebraic Stacks.

Macaca nigra self-portrait
Lecture 1: introducing the ideas of stacks. parametrizing elliptic curves with the j-line. functors on schemes.
Lecture 2: properties of morphisms.
Lecture 3: schemes via Zariski gluing of sheaves.
Lecture 5: Topoi, sites and points.
Lecture 6: Fibered Categories, part 1.
Lecture 7: Fibered Categories, part 2.
Lecture 8: Fibered Categories, part 3.
Lecture 9: Fibered Categories, part 4/Descent, part 1.
Addendum 1: The Isom Presheaf.
Lecture 10: Descent, part 1.5.
Lecture 11: Descent, part 2.
Lecture 12: Descent, part 3.
Lecture 13: Descent, part 4.
Lecture 14: Descent, part 5
Lecture 15: End of descent, beginning of algebraic spaces
Lecture 16: Algebraic spaces. Definitions, constructions and examples
Lecture 18: Properties of algebraic spaces
Lecture 19: Sprint through algebraic spaces, part 1
Lecture 20: From algebraic spaces to algebraic stacks
Lecture 21: Stacks, spaces and fiber products
Lecture 22: Properties of stacks and morphisms of stacks
Lecture 23: Properties of morphisms of stacks, inertia and Deligne-Mumford stacks
Lecture 24: Deligne-Mumford stacks and moduli of curves
Lecture 25: Moduli of curves
Lecture 26: Moduli of curves of general type is Deligne-Mumford. Stacks over stacks.
Lecture 27: Cohomology of quasi-coherent sheaves on algebraic stacks.
Lecture 28: Properties of stacks and morphisms between them.
Lecture 29: Root stacks, coarse moduli and gerbes.