18.726 | Spring 2009 | Graduate

Algebraic Geometry

Lecture Notes

The notes below were discussed in the lectures specified in the table. As indicated, some notes spanned more than one lecture, and some lectures covered topics from more than one set of lecture notes.

1 Introduction and overview (PDF)
2 Basics of category theory (PDF)
3-5 Sheaves (PDF)
5 Abelian sheaves (PDF)
6-7 Schemes (PDF)
7-9 Morphisms of schemes (PDF)
9-10 Sheaves of modules (PDF)
11-12 More properties of morphisms (PDF)
12-13 Projective morphisms, part 1 (PDF)
13-14 Projective morphisms, part 2 (PDF)
15 More properties of schemes (PDF)
16-17 Flat morphisms and descent (PDF)
17-18 Differentials (PDF)
18-19 Divisors (PDF)
19-20 Divisors on curves (PDF)
21-23 Homological algebra (PDF)
24-26 Sheaf cohomology (PDF)
27 Cohomology of quasicoherent sheaves (PDF)
27-29 Cohomology of projective spaces (PDF)
29-30 Hilbert polynomials (PDF)
30-33 GAGA (PDF)
33-34 Serre duality for projective space (PDF)
35-36 Dualizing sheaves and Riemann-Roch (PDF)
36-37 Cohen-Macaulay schemes and Serre duality (PDF)
38 Higher Riemann-Roch (PDF)
39 Étale cohomology (PDF)

These notes on spectral sequences and Cech cohomology were not covered during lecture (PDF).

Course Info

As Taught In
Spring 2009
Learning Resource Types
Problem Sets
Lecture Notes