Instructor: David Nadler
Office Hours: Tuesdays, 2-3:30pm, 815 Evans, or by appointment.
Lectures: Tuesdays and Thursdays 11am-12:30pm, Dwinelle 109.
Course number: 22337
Prerequisites: Math 250A-250B or equivalent familiarity with abstract algebra.
Sources:
Syllabus: This will be an introduction to (primarily complex) algebraic geometry in the language of schemes.
- Categories (FOAG, Chapter 1).
- Sheaves (FOAG, Chapter 2).
- Affine schemes (FOAG, Chapter 3).
- Schemes (FOAG, Chapter 4).
- Properties of schemes (FOAG, Chapter 5).
- Morphisms of schemes (FOAG, Chapter 6 and some of Chapters 7-9).
- Varieties (FOAG, Chapter 10).
- Dimension, smoothness (FOAG, some of Chapters 11-12).
Evaluation:
There will be weekly homeworks and a quiz, a midterm, and a final exam.
Exams:
Due Thursday 10/24: Midterm.
Due Tuesday 12/17: Final.
Homework:
- Due Tuesday 9/3: Read FOAG 1.1-1.6. Exercises FOAG 1.2.D, 1.3.B, 1.3.C-1.3.F, 1.3.H, 1.3.S, 1.3.U, 1.3.Z(c), 1.4.B, 1.4.D, 1.4.F, 1.5.C, 1.5.E, 1.5.H, 1.6.F, 1.6.J.
- Due Tuesday 9/10: Read FOAG 2.1-2.4. Exercises FOAG 2.1.A, 2.2.B, 2.2.D, 2.2.F, 2.2.J, 2.3.C, 2.3.D, 2.3.I, 2.3.J, 2.4.A, 2.4.B, 2.4.C, 2.4.D, 2.4.E, 2.4.F, 2.4.M, 2.4.N, 2.4.O, 2.4.P.
- Due Tuesday 9/17: Read FOAG 2.5-2.7. Exercises FOAG 2.5.A-G, 2.5.J, 2.6.A-G, 2.7.A, 2.7.C, 2.7.D.
- Due Tuesday 9/24: Read FOAG 3.1-3.4. Exercises FOAG 3.2.A-E, 3.2.F-H, 3.2.J-L, 3.2.M-Q, 3.2.R-T,
3.4.A-K, 3.5.A-F.
- Due Tuesday 10/1: Read FOAG 3.5-4.1. Exercises FOAG 3.5.A-F, 3.6.A-T, 3.7.A-G, 4.1.D.
- Due Tuesday 10/8: Read FOAG 4.2-4.5. Exercises FOAG 4.3.A-G, 4.4.A-F, 4.5.A-Q.
- Due Tuesday 10/15: Read FOAG 5.1-5.4. Exercises FOAG 5.1.A-E, 5.2.A-I, 5.3.B-I, 5.4.A-D
- Due Tuesday 11/5: Read FOAG 21.1-4. Exercises FOAG 21.2.A-U, 21.3.A, 21.4.A.
Quizzes:
- Due Thursday 9/5: Quiz 1.
- Due Thursday 9/12: Quiz 2.
- Due Thursday 9/19: Quiz 3.
- Due Thursday 9/26: Quiz 4.
- Due Thursday 10/3: Quiz 5.
- Due Thursday 10/10: Quiz 6.
- Due Thursday 11/7: Quiz 7.
- Due Thursday 11/14: Quiz 8.
- Due Thursday 11/21: Quiz 9.