This course will cover advanced topics in the theory of schemes with an emphasis on examples. We will cover themes not usually covered in UW's first year algebraic geometry course. Topics include:
- Representability of Grassmanian, Hilbert, and Quot functors.
- Cohomology of sheaves on schemes and its relation with the derived category including the finiteness theorem that the derived pushforward along a proper morphism preserves coherence
- Cohomology and base change theorems and their applications to moduli theory
- Deformation theory: infinitesimal deformation theory, higher order deformations and obstructions, Schlessinger's theorem and the cotangent complex