DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-12

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.

Morphisms of classical affine varieties

Definition

Let $X$ and $Y$ be classical affine varieties over an algebraically closed field $k$ . A map $φ : X \to Y$ is a morphism when for every open subset $V \subseteq Y$ and every regular function $f \in O_{Y} (V)$ , the pullback $f \circ φ : φ^{- 1} (V) \to k$ is regular on $φ^{- 1} (V)$ .

Because $Y$ is affine, it is enough to test pullback on global regular functions. By Global regular functions on a classical affine variety are its coordinate ring, those are exactly the elements of $k [Y]$ .

Morphisms of classical affine varieties

Definition

Depends on

Dependency tree · 2 levels

Sources