Week of	Topics
8/25	Algebraic sets and algebraic equations. Examples: affine space, units, hypersurfaces
9/1	D_I, Projective space.The functorial point of view. Affine algebraic spaces.
9/8	Noether normalization and the Nullstellensatz. The Zariski topology.
9/15	Localization. presheaves and sheaves.
9/22	The structure sheaf. The category of schemes.
9/29	Gluing Schemes. Sheaves of modules. Quasicoherence.
10/06	Quasicoherence. Quasi-compact, quasi-separated, and affine morphisms
10/13	Closed and open immersions; more gluing. Tensor products and fibered products. Fibers of a morphism.
10/20	VE. PE, Proj. Projective morphisms, divisors
10/27	The diagonal. Injectivity and surjectivity. Finiteness.
11/03	Separated, affine, and finite type morphisms.Proper morphisms.
11/10	Dimension. Normality and regularity.
11/17	Differentials and calculus
11/24	Smooth and flat morphisms
12/02

The above schedule is just a rough guide and subject to change as the course progresses.