Math 533                                           Section 201,    Spring 2017

Algebraic Geometry II

Time/Place:  TuTh  12:30-14:00,  MATX 1102

Instructor:  K. Behrend

Office Hours:  After Class.
Math Annex 1213.

Prerequisites: Math 532 is not a prerequisite. A certain level of familiarity
with geometry, topology, and algebra is however expected.

Syllabus: Schemes.

We will cover Chapters 2 and 3 of Hartshorne's Algebraic Geometry.
1. Sheaves. 1.
2. Schemes. 2-3.
3. First Properties. 4.
4. Separation and Properness. 5-6.
5. Modules. 7-8.
6. Divisors. 9-10.
7. Projective Morphisms. 11-12.
8. Differentials. 13.
9. Derived Functors & Cohomology. 14
10. Noetherian Affine Schemes & Cech Cohomology. 15
11. Projective Space. 16
12. Ext. 17
13. Serre Duality. 18-19
14. Higher Direct Images. 20.
15. Flatness. 21.
16. Smoothness. 22.
17. Formal Functions. 23.
18. Semicontinuity. 24.
Homework: Your course mark will be based on homework assignments.

I would like you to not hand in complete solutions, but
rather sketches of solutions. For now, the guideline is: no more than
100 words per problem (or problem part for multi-part problems).
Think of writing notes to yourself that would allow you to reconstruct
your solution in half a year (or three years). It is entirely
permissible to answer a question with a phrase like `follows by
tedious work directly from the defintions', if that is, indeed, the
case. Rather than writing down a calculation, try to state the reason
why the calculation works.

I'm aware that this approach doesn't always work, but let's try it as
much as we can.

Hartshorne Chapter II:
1. Due January 12: 1.2, 1.3, 1.14, 1.15.
2. Due January 19: 2.3, 2.4, 2.7, 2.8, 2.19.
3. Due February 2: 3.7, 3.8, 3.15, 3.19, 4.1, 4.2, 4.4.
4. Due March 2: 5.6, 5.7, 5.8, 6.1, 6.11, 6.12, 7.1, 7.4, 7.12.
5. Due March 30: 8.3, 8.5, 8.7.
6. Due April 6: