Alphabeta MathHow 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.
An infinite disjoint union is locally but not globally finite type
Statement refuted
Every locally finite-type morphism is finite type.
Facts & Assumptions
Given: A field .
A finite-type morphism is locally of finite type and quasi-compact Locally finite type and finite type morphisms.
Counterexample
Let and map it to . Each component is an affine finite-type chart, so the map is locally of finite type.
The inverse image of the one-point base is covered by the open components, and no finite subfamily covers . Thus the map is not quasi-compact; by [F1] it is not finite type.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- The Stacks Project, Morphisms of Schemes, Definition 15.1 (standard reference, not scraped)