Schedule
- Thursday; Waterman 423, 11:35 a.m. - 1:00 p.m. (during unQVNTS
weeks)
- Wednesday, Friday; Waterman 423, 3:30 p.m. - 4:30 p.m.
Vakil Notes
Speaking Order
The idea is to follow Ravi's 2011-2012 outline as close as possible. In
particular we want to cover all of the "important exercises" from, say, the
2005-2006 notes. Speakers have discretion of where they want to pick their
problems from.
- Dupuy (Wed, 8/28): So we didn’t finish all of the category theory we
wanted to (of course) but covered a lot. We still need to talk about
adjoint functors and preservation of limits. We did end up talking about
Yoneda’s Lemma.
- Dupuy (Fri, 8/30): Limits, preservation of limits. Problem:
1.3W, 1.3Y, 1.4D (did this is Algebra 4), 1.4F (did this in Algebra
4), 1.5H
- Hilado (Wed, Friday): We covered abelian categories, adjoint
functors, presheaves, sheaves and their morphisms, stalks, germs, and
sheafification. As an example of sheafification we looked at the
constant presheaf vs. the constant sheaf on the two-element set with the
discrete topology.
- Vincent (Wed 9/11): Topology of Spec(R)
- Vincent (Fri 9/13): Topology of Spec(R)
- (Backman, Wed 9/18. 3.6, 3.7, 4.1, 4.2, 4.3 of Book):
- (Dupuy, Th 9/19): Schemes, Examples of Schemes (including Proj)
- (Backman, Fri 9/20): Topology of Spec(A)
- (Dupuy, Wed 9/25): Problems.
- (Problems, Thu 9/26): Sheaf for Spec(A), rational normal curve
- (Dupuy, Fri 9/27): Normality and Factorality
- (Franklin, Wed 10/2): quasi-separatedness, reducedness, integrality,
affine-local properties (Noetherian, finite type etc)
- (Th 10/3): PROBLEMS
- (Franklin, Fri 10/4): More on affine-local properties
- (Dupuy, Wed 10/9): Cokernels and Cocyles
- (Dupuy, Fri 10/11): Cokernels and Cocyles
- (Dupuy, Wed 10/16): Morphisms to a Fixed Scheme is a Sheaf
- (Th 10/17): PROBLEMS
- (Dupuy, Fri 10/18): Morphisms to a Fixed Scheme is a Sheaf
- (Hilado, Wed 10/23): Functor of Points
- (Hilado, Fri 10/25): More on the Functor of Points
- (Hilado, Wed 10/30): More on the Functor of Points
- (Th 10/31): PROBLEMS
- (Dupuy, Fri 11/1): Flatness of Modules and Schemes
- (Dupuy, Wed 11/6): More on Flatness of Modules and Schemes
- (Dupuy, Fri 11/8): Open and Closed Immersions
- (Dupuy, Wed 11/13): Open and Closed Immersions
- (Th 11/14): PROBLEMS
- (Hilado, Fri 11/15): Fibered Products of Schemes
- (Hilado, Wed 11/20): More on Fibered Products of Schemes
- (Hilado, Fri 11/22): More on Fibered Products of Schemes
- (Rehm, Wed 11/27): Computing Fibered Products
- (Hilado, Fri 11/29): Representable Functors and the Representability Criterion
- (Franklin, Wed 12/4): Proj of Graded Rings
- (Th 12/4): PROBLEMS
- (Franklin, Fri 12/6): More on Proj of Graded Rings