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.

Scheme-theoretic inverse images of subschemes

Definition

For $f : X \to S$ and a closed or locally closed subscheme $Z ↪ S$ , define the scheme-theoretic inverse image to be $X \times_{S} Z \to X$ . By Base change of immersions it is a closed or locally closed subscheme, respectively. For a closed ideal sheaf $I$ , the inverse-image ideal is $Im (f^{*} I \to O_{X})$ . For an open subscheme this construction is the open inverse image with its restricted sheaf.

Scheme-theoretic inverse images of subschemes

Definition

Depends on

Dependency tree · 2 levels

Sources