# AG-Week Five

From UW-Math Wiki

# 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.)