Topics in Algebraic Geometry 2023/24

These are some rough notes for the Topics in Algebraic Geometry reading group at the University of Leeds.

To-do list

• Sections
  • Affine Schemes
    • Comment about Spec A where A is the ring of continuous real functions on a space
    • Consider Spec ℤ and Spec ℤ[x]
    • Non-examples of affine schemes
      • A^2/{0}
      • A \sqcup A/(A \ {0}) (line with two origins)
  • Proj
    • Write down what a homogeneous ideal is
    • Write down what it means to be generated by homogeneous ideals
    • Explicitly write down how to cover Proj by affine spaces
  • Spec ℤ[x]
• Comments
  • Dimension of schemes
    • Krull
    • Tangent spaces
    • Functor of points