Week of	Topics
1/19	Introduction to cohomology. Ext and Abelian categories
1/26	Complexes, cones and triangulated categories
2/02	Derived functors and derived categories. Sheaf cohomology.
2/09	Flasque sheaves. Cech cohomology.
2/16	Affine space. Projective space.
2/23	Finiteness of cohomology
3/02	Serre-Grothendieck duality
3/09	Perfection, cohomology and base change
3/16	Divisors, maps to projective space
3/23	Spring Break
3/30	Curves, Riemann-Roch
4/06	Hurwitz's theorem. Projective embeddings
4/13	The canonical embedding
4/20	Surfaces, Riemann-Roch,
4/27	Zeta functions
5/11	Applications

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