DefinitionDefinition: Literature-sourcedProof: Not applicablejudge 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.

Locally finite type and finite type morphisms

Definition

A morphism $f : X \to S$ is locally of finite type if every point of $X$ has an affine open neighbourhood $U$ and $f (U)$ lies in an affine open $V = Spec A$ of $S$ such that $U = Spec B$ and $A \to B$ is of finite type. It is of finite type if it is locally of finite type and quasi-compact.

Depends on

Dependency tree · 2 levels

Sources

The Stacks Project, Morphisms of Schemes, Definition 15.1