Maths blogs:

Algebraic geometry “megaprojects”:

  • Ravi Vakil’s Foundations of Algebraic Geometry course is a huge, well-written and very readable book, freely available to download and constantly updated. It takes a categorical viewpoint from the start, which suits me well. It also doesn’t assume an encyclopaedic knowledge of commutative algebra unlike other algebraic geometry books.
  • Vakil’s notes are extensive, but the Stacks Project is on another level altogether. It’s a colossal, nearly 5000-page text developing all the theory needed to study algebraic geometry and algebraic stacks, which are even more general objects than schemes. It’s not something you’d want to read cover-to-cover, but because it is entirely self-contained and develops commutative algebra, category theory and geometry entirely from scratch, it is an excellent place to go to read a chapter and become more enlightened.