DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-09

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

A rational map as an equivalence class of morphisms on nonempty opens

Definition

For affine varieties $X, Y$ , a representative of a rational map $X ⇢ Y$ is a pair $(U, ϕ)$ with $U \subseteq X$ nonempty open and $ϕ : U \to Y$ a morphism. Two pairs represent the same rational map when their maps agree on some nonempty open subset of their common domain. A rational map is an equivalence class for this relation; its equivalence-relation well-definedness is supplied by The rational-map relation is transitive ↗. The domain of a representative need not be all of $X$ .

Sources

Source comparison: Milne, Algebraic Geometry, v6.10, §5l p. 117. Conventions here distinguish arbitrary affine algebraic sets from nonempty irreducible varieties.

Depends on

Dependency tree · 2 levels

Sources

J. S. Milne, Algebraic Geometry v6.10, §5l p. 117