Advanced Algebraic Geometry

1. i (Pre-)sheaves; sheaves of modules over topological spaces.
2. ii Spectrum of a ring; stalks; coordinate rings; dimension.
3. iii Schemes; gluing; reduced and integral schemes.
4. iv Products; separated and proper schemes.
5. v Projective morphisms; flat morphisms; birational maps.
6. vi Coherent sheaves and vector bundles; divisors and line bundles.
7. vii Sheaf cohomology; derived push-forward and pull-back; base change.
8. viii Serre duality theorem; semicontinuity theorems.
9. ix Functor of points; group schemes; Hilbert schemes.

Course syllabus (PDF)

1. 01 Assignment 1 PDF ↗