Lecture Notes · Lecture Notes
MIT OpenCourseWare
Algebraic Geometry
Art: Max Brückner (1860 – 1934), Brückner Vielflache Tafel 07 · Public domain
- Instructor
- Prof. Kiran Kedlaya
- Term
- Spring 2009
- Level
- Graduate
- What's inside
- 12 problem sets · 1 lecture note · 27 other files · 3 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.726 Algebraic Geometry, Spring 2009, Prof. Kiran Kedlaya — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.
Not included here
2 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely.
- Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence.
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Lecture Notes
27 files
- Introduction Download
- Category theory Download
- Sheaves Download
- More on abelian sheaves Download
- Schemes Download
- Morphisms of schemes Download
- Sheaves of modules Download
- More properties of morphisms Download
- More properties of schemes Download
- Flat morphisms and descent Download
- Differentials Download
- Divisors, linear systems, and projective embeddings Download
- Divisors on curves and Riemann-Roch Download
- Homological algebra Download
- Sheaf cohomology Download
- Cohomology of quasicoherent sheaves Download
- Cohomology of projective space Download
- Hilbert polynomials and flatness Download
- Spectral sequences and Čech cohomology Download
- GAGA Download
- Serre duality for projective space Download
- Dualizing sheaves and Riemann-Roch Download
- Cohen-Macaulay schemes and Serre duality Download
- Higher Riemann-Roch Download
- Étale cohomology Download
- Projective morphisms, part 1 Download
- Projective morphisms, part 2 Download
Assignments
Course outline
Lecture Notes · Lecture Notes
Lecture 2: Basics of category theory ( PDF )
Lecture Notes · Lecture Notes
Lecture 5: Abelian sheaves ( PDF )
Lecture Notes · Lecture Notes
Lecture 15: More properties of schemes ( PDF )
Lecture Notes · Lecture Notes
Lecture 27: Cohomology of quasicoherent sheaves ( PDF )
Lecture Notes · Lecture Notes
Lecture 38: Higher Riemann-Roch ( PDF )
Lecture Notes · Lecture Notes
Lecture 39: Étale cohomology ( PDF )
MIT OpenCourseWare, Prof. Kiran Kedlaya, 18.726 Algebraic Geometry, Spring 2009.
License: CC BY-NC-SA 4.0 · Edition: Spring 2009 · Open the original course on OCW ↗
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