Math 256A, Algebraic Geometry, Fall 2017

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.

  1. Categories (FOAG, Chapter 1).
  2. Sheaves (FOAG, Chapter 2).
  3. Affine schemes (FOAG, Chapter 3).
  4. Schemes (FOAG, Chapter 4).
  5. Properties of schemes (FOAG, Chapter 5).
  6. Morphisms of schemes (FOAG, Chapter 6 and some of Chapters 7-9).
  7. Varieties (FOAG, Chapter 10).
  8. 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:

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Due Tuesday 10/8: Read FOAG 4.2-4.5. Exercises FOAG 4.3.A-G, 4.4.A-F, 4.5.A-Q.
  7. 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
  8. Due Tuesday 11/5: Read FOAG 21.1-4. Exercises FOAG 21.2.A-U, 21.3.A, 21.4.A.

Quizzes:

  1. Due Thursday 9/5: Quiz 1.
  2. Due Thursday 9/12: Quiz 2.
  3. Due Thursday 9/19: Quiz 3.
  4. Due Thursday 9/26: Quiz 4.
  5. Due Thursday 10/3: Quiz 5.
  6. Due Thursday 10/10: Quiz 6.
  7. Due Thursday 11/7: Quiz 7.
  8. Due Thursday 11/14: Quiz 8.
  9. Due Thursday 11/21: Quiz 9.