Skip to main content
Post Made Community Wiki
Source Link
Zack Wolske
  • 1.9k
  • 15
  • 21

If you are comfortable doing a lot of exercises, and even better if you can work with a group, then I recommend Ravi Vakil's notes for his course, which are frequently updated and can be found here: http://math.stanford.edu/~vakil/216blog/ It is a hands-on treatment, and works through many facts you would need from commutative algebra and category theory.

From the introduction:

"Attempts to explain algebraic geometry often leave such background to the reader, refer to other sources the reader won’t read, or punt it to a telegraphic appendix. Instead, this book attempts to explain everything necessary, but as little possible, and tries to get across how you should think about (and work with) these fundamental ideas, and why they are more grounded than you might fear."

"The book is intended to be as self-contained as possible. I have tried to follow the motto: “if you use it, you must prove it”. I have noticed that most students are human beings: if you tell them that some algebraic fact is in some late chapter of a book in commutative algebra, they will not immediately go and read it. Surprisingly often, what we need can be developed quickly from scratch, and even if people do not read it, they can see what is involved."