Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.fpqcPrecoverage
CategoryTheory.Precoverage AlgebraicGeometry.Scheme
The fpqc precoverage on the category of schemes is the quasi-compact precoverage on flat morphisms. The covering families are jointly-surjective, quasi-compact families of flat morphisms.
- Defined in
- Mathlib.AlgebraicGeometry.Sites.Fpqc
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CategoryTheory.Precoveragestatement · cited by 204
- AlgebraicGeometry.Flatproof · cited by 49
- AlgebraicGeometry.Scheme.propQCPrecoverageproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.fpqcTopologyproof · cited by 6
- AlgebraicGeometry.Scheme.fppfPrecoverage_le_fpqcPrecoveragestatement · cited by 2
- AlgebraicGeometry.Scheme.zariskiPrecoverage_le_fpqcPrecoveragestatement · cited by 1
- AlgebraicGeometry.Scheme.proetalePrecoverage_le_fpqcPrecoveragestatement · cited by 1
- AlgebraicGeometry.Scheme.Hom.singleton_mem_fpqcPrecoveragestatement · cited by 0