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.
External classification of torsors by first cohomology
PDF p. 4: Weight one units and Picard identification
Statement
For an abelian sheaf on a small site with terminal object and the derived-cohomology conventions of Derived global sections on a scheme site, there is a canonical bijection from isomorphism classes of -torsors to . A torsor is a locally nonempty sheaf of sets with a simply transitive -action on each nonempty section set.
External input
This is Stacks Project Lemma 21.4.3, imported with the reading limits stated above. Its proof is not claimed as a local reconstruction.
Depends on
Dependency tree · 3 levels
Arrows run from prerequisites to the items that use them. External source nodes link directly to the cited text. The view shows up to three dependency steps; open a prerequisite to continue.
External dependencies
For an abelian sheaf on a site, isomorphism classes of its torsors are canonically in bijection with first sheaf cohomology.
Hypotheses: A site and an abelian sheaf, with the usual sheaf cohomology and size conventions.
Reading limits: The statement and displayed construction in the proof were read. The source explicitly omits verification that its two constructions are inverse; that verification was not reconstructed here.
Sources
- The Stacks Project, First cohomology and torsors · Lemma 21.4.3 and its proof