Sheaves on spaces. Spec(R), affine schemes. Locally ringed spaces. Scheme = locally affine. Structure sheaf Oₓ.
graph TD
D1["Def: Presheaf\nF: Opens→Ab"]
D2["Def: Sheaf\nglue + unique"]
D3["Def: Spec R\nprime ideals + topol"]
D4["Def: Affine scheme\nSpec R, Õₘ"]
T1["Thm: Stalk Oₓ\nlocal ring"]
T2["Thm: ΓSpecR Õₘ ≅ R"]
T3["Thm: Scheme\nlocally affine"]
T4["Thm: Morphism\nring hom → cont map"]
T5["Thm: Proj S\nprojective scheme"]
D1 --> D2
D3 --> D4
D2 --> T3
D4 --> T1
D4 --> T2
D4 --> T3
T3 --> T4
T3 --> T5
classDef definition fill:#b197fc,color:#fff
classDef theorem fill:#51cf66,color:#fff
class D1,D2,D3,D4 definition
class T1,T2,T3,T4,T5 theorem
Process Statistics
- Nodes: 14
- Edges: 11
- Definitions: 4
- Theorems: 5
Frontier: Stacks, derived schemes, non-archimedean geometry. math.AG