AG-Week Five: Difference between revisions
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== Questions == | == Questions == | ||
* Cohen-Macaulay rings, and dimensions. | * 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 == | == 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.) | * 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.) | ||
== Typos == | == Typos == | ||
[[Category:Fall 2010 Algebraic Geometry Reading Course]] | [[Category:Fall 2010 Algebraic Geometry Reading Course]] | ||
Latest revision as of 19:03, 1 October 2010
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.)