Separation axioms,” Section 26.21¶
Authors, T. S. P. Separation axioms,” Section 26.21.
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Domain-specific¶
- Fiber Product of Schemes
- If affine-locally they are cut out by ideals \(I,J\subset A\), their intersection is \(\operatorname{Spec}(A/(I+J))\), because \((A/I)\otimes_A(A/J)\cong A/(I+J)\). Inverse images of closed subschemes, equalizers, diagonals, and tests for separatedness are built from the same squares.
This sourceDevelops diagonal morphisms, equalizers, and separatedness through fiber-product diagrams.
- If affine-locally they are cut out by ideals \(I,J\subset A\), their intersection is \(\operatorname{Spec}(A/(I+J))\), because \((A/I)\otimes_A(A/J)\cong A/(I+J)\). Inverse images of closed subschemes, equalizers, diagonals, and tests for separatedness are built from the same squares.
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