DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07

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.

Affine morphisms

Definition

A morphism of schemes $f : X \to S$ is affine when $f^{- 1} (U)$ is affine for every affine open subscheme $U \subseteq S$ . Here the inverse image carries the restricted structure sheaf, as in Affine open subschemes, and $f$ is a morphism of locally ringed spaces as in Morphisms of schemes. The empty scheme is affine, being $Spec 0$ . Affineness of a morphism does not require its total source or target to be affine.

Depends on

Dependency tree · 2 levels

Sources

Stacks 29.11.1