Lecture 12: Schemes

We covered 12.22–12.41 of Gathmann's notes.

• Locally ringed spaces.
• Affine schemes as locally ringed spaces (Prop 12.27).
• Closed subschemes of affine schemes.
• Distinguished open subschemes (Prop 12.29) of affine schemes.
• Schemes. Open and closed subschemes. Fiber products.
• Properties of schemes: finite type, reduced, separated.

Suggested exercises: 12.35, 12.42, 12.43 (that is, all).