AG-Week Five

Week Five

This is the page with specific information for Week 5 of our Algebraic Geometry Graduate Reading Course. This week we will be finishing up sheaves and start our official introduction to schemes.

Discussion Leader: Evan

Schedule

Week five

• For 9/29: Read sections 4.1 and 4.2 of the notes.
• For 10/1: Read sections 4.3, 4.4, and 4.5 of the notes.
• For 10/4: Breather / discuss previous material.
  • Meeting with faculty.

Homework

Six problems are due on 9/29.

Questions

• Cohen-Macaulay rings, and dimensions.
• What kinds of topological spaces can be Spec of a ring?
• What kinds of topological properties of Spec R translate "reasonably" to properties of R? (E.g., Spec R being disconnected implies R is a direct product of two rings.)

Comments

• Localization notation is confusing. Be very careful about the difference between localizing at an element, and localizing "at" a prime ideal. (The latter really means localizing at the multiplicative system of all elements not in the prime ideal.)