Textbooks of scheme theory with detailed proof, no classical algebraic geometry and so on

346 Views Asked by At

I would like to learn scheme theory. But it seems that there are many books of scheme theory, so I look for the textbooks that satisfied my below conditions:

  1. not so particular about classical algebraic geometry.
  2. proofs is detailed
  3. category theory, abelian category and homology algebra are premised
  4. prepare for abelian varieties and arithmetic geometry

If you know the textbooks satisfied such conditions, I hope you'll tell me. I'd appreciate if you could answer the question.

1

There are 1 best solutions below

3
On BEST ANSWER

I don't know what you mean by classical algebraic geometry but Lius book "Algebraic Geometry and Arithmetic Curves" is a very good reference.
I still think Hartshorne chapter 2 is a must for everyone doing algebraic geometry. There are a few books coming from lectures: Rave Vakils tremendously detailed lecture notes "The Rising Sea" for example. More formally, Scholzes notes "Algebraic Geometry" when he gave the class.
These are not official notes, but can be found online.