Schedule

All Readings are from Vakil’s “Rising Sea.”  There will be about 7 pages of text covered in each meeting.

Meetings 1-6 (Chapter 1, Categories)

  1. Overview
  2. categories and functors
  3. universal properties (Jan 15)
  4. (1.4) limits and colimits (Wed Jan 20)
  5. (1.5) adjoints (Fri Jan 22)
  6. (1.6) abelian categories (Mon Jan 25)

Meetings 7-11 (Chapter 2, Sheaves)

  • up through 2.2.6 (Wed Jan 27)
  • up through 2.3.D (Fri Jan 29)
  • up through 2.4.8 (Mon Feb 1)
  • finish 2.4 (Wed Feb 3)
  • (2.5, 2.6) (Friday Feb 5)

Meetings 12-16 (Chapter 3, affine schemes as topological spaces)

  • (3.2) affine schemes as sets (Friday Feb 12)
  • (3.2,3.3) visualizing points (Mon Feb 15)
  • (3.4,3.5) the topology on Spec R (Wed Feb 17)
  • (3.6) Noetherian properties (Fri Feb 19)
  • (3.6,3.7) “V” and “I” (Mon Feb 22)

Meetings 17-19 (Chapter 4, definition of schemes)

  • (4.1,4.2) the structure sheaf and visualizing nilpotents (Wed Feb 24)
  • (4.3,4.4) definition of schemes and examples (Fri Feb 26)
  • (4.5) projective schemes (Mon Feb 29)

Meetings 20-22 (Chapter 5, some properties of schemes)

Meetings 23-26 (Chapter 6, morphisms of schemes)

Meetings 27-29 (Chapter 7, useful classes of morphisms and schemes)

(Skip chapter 8.)

Meetings 30-33 (Chapter 9, fibered products)

Meetings 34-37 (Chapter 10, separated and proper morphisms, and varieties)

(Skip chapter 11.)

Meetings 37-40 (Chapter 12, regularity and smoothness)