Algebraic Geometry
This MIT OpenCourseWare course continues from 18.725 Algebraic Geometry into the language of schemes, properties of morphisms, and sheaf cohomology. It builds the technical toolkit of modern algebraic geometry, covering topics such as affine and projective schemes, quasi-coherent sheaves, and cohomological methods used to study geometric objects algebraically. Materials include lecture notes and problem sets drawn from MIT's graduate mathematics curriculum, giving students the chance to work through proofs and constructions at the level expected in a research-oriented course. No video lectures are included, but the written notes are detailed enough to follow the course's logical progression from schemes to cohomology. The course assumes familiarity with the prerequisite material on varieties and morphisms, and is aimed at students who already have a working knowledge of commutative algebra and basic algebraic geometry. All materials are free to access under MIT OpenCourseWare's license.