|
Week |
Date |
Section(s) |
Homework Due Dates
(Fri at 11:59PM) |
| 1 | 1/13 | Categories
(3.1), Sheaves (2.1) |
|
| 1/15 | Sheaves, Sheafification (2.1) | Homework 1 | |
| 2 | 1/20 |
Sheaves of modules (2.5), Abelian categories (3.1),
Mod(OX) is Abelian (2.5) |
|
| 1/22 | Grothendieck Abelian categories, Injective objects (3.1) | Homework 2 | |
| 3 | 1/27 | Grothendieck Abelian categories have enough injectives, Mod(OX) is Grothendieck Abelian (3.2) | |
| 1/29 | Derived functors and sheaf cohomology, Grothendieck's vanishing theorem (3.2) | Homework 3 | |
| 4 | 2/3 | Coherent and quasi-coherent sheaves (2.5), Affine schemes (2.2), Serre's equivalence for affine schemes (2.5) | |
| 2/5 | Cartan's Theorem
B for affine schemes (3.3), Schemes (2.2) |
Homework 4 | |
| 5 | 2/10 | Noetherian schemes, immersions, reduced schemes (2.2–2.3) | |
| 2/12 |
The qcqs lemma (2.5), Serre's criterion for affineness (3.3) |
Homework 5 | |
| 6 | 2/17 |
Proj (2.2), Sheaves associated to graded modules (2.5) |
|
| 2/19 | Graded modules associated to sheaves, Serre's equivalence for QCoh(Proj(S)) (2.5) | Homework 6 | |
| 7 | 2/24 |
Serre's equivalence for Coh(Proj(S)) (2.5), Serre's finiteness and vanishing theorems (2.5, 3.5), Fiber products (2.3) |
|
| 2/26 | Fiber products and base change (2.3) | ||
| 8 | 3/3 | Base change
(2.3), The diagonal morphism and separated morphisms (2.4) |
Homework 7 |
| 3/5 | Separated
morphisms (2.4), Čech cohomology (3.4) |
||
| 9 | 3/10 | The Cohomology of Projective Space (3.5) | |
| 3/12 | No Class - Class Release for Midterm Exam | Midterm Oral
Exam 3/12 and 3/13 |
|
Spring break |
|||
| 10 | 3/24 | Valuative criteria (2.4) | |
| 3/26 | Valuative
criteria (2.4), Relative Proj (2.7) |
Homework 8 | |
| 11 | 3/31 | Rational maps to
relative Proj (2.7) Ample and very ample invertible sheaves (2.5, 2.7) |
|
| 4/2 | Projective morphisms (2.7) | Homework 9 | |
| 12 | 4/7 | Divisors (2.6) | |
| 4/9 | Divisors (2.6) | Homework 10 | |
| 13 | 4/14 | Divisors (2.6) | |
| 4/16 | Divisors
(2.6) Ampleness criteria (2.7, 3.5) |
Homework 11 | |
| 14 | 4/21 | Ampleness
criteria (2.7, 3.5) Blowups (2.7) Flat morphisms (3.9) |
|
| 4/23 | Differentials (2.8) | Homework 12 | |
| 15 | 4/28 |
Differentials (2.8), Formally smooth morphisms (3.10) |
|
| 4/30 | Jacobian
criterion, Bertini's theorem (2.8), Serre duality (3.7), Riemann–Roch for curves (4.1) |
||
| 16 | Have a wonderful summer! |
||