Algebraic Geometry II
Time/Place: TuTh 12:30-14:00, MATX 1102
Instructor: K. Behrend
Office Hours: After Class.
Math Annex 1213.
Math 532 is not a prerequisite. A certain level of familiarity
with geometry, topology, and algebra is however expected.
We will cover Chapters 2 and 3 of Hartshorne's Algebraic
Your course mark will be based on homework assignments.
- Sheaves. 1.
- Schemes. 2-3.
- First Properties. 4.
- Separation and Properness. 5-6.
- Modules. 7-8.
- Divisors. 9-10.
- Projective Morphisms. 11-12.
- Differentials. 13.
- Derived Functors & Cohomology. 14
- Noetherian Affine Schemes & Cech Cohomology. 15
- Projective Space. 16
- Ext. 17
- Serre Duality. 18-19
- Higher Direct Images. 20.
- Flatness. 21.
- Smoothness. 22.
- Formal Functions. 23.
- Semicontinuity. 24.
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:
- Due January 12: 1.2, 1.3, 1.14, 1.15.
- Due January 19: 2.3, 2.4, 2.7, 2.8, 2.19.