DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-06

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.

The underlying space of an affine spectrum

Definition

All rings below are commutative with $1$ . For a ring $A$ , the underlying topological spectrum is the Zariski space whose points are the prime ideals of $A$ ; its basic opens are $D (f) = {p : f \notin p}$ . This notation is deliberately topological until the structure sheaf is constructed. For $A = 0$ there are no proper prime ideals, so this space is empty.

Depends on

Dependency tree · 2 levels

Sources

The Stacks Project, Section 26.5