Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.zariskiPrecoverage
CategoryTheory.Precoverage AlgebraicGeometry.Scheme
The Zariski precoverage on the category of schemes is the precoverage defined by jointly surjective families of open immersions.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 105 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
- AlgebraicGeometry.IsOpenImmersionproof · cited by 476
- AlgebraicGeometry.Scheme.precoverageproof · cited by 336
- CategoryTheory.Precoveragestatement · cited by 204
Cited by12
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsZariskiLocalAtSourceproof · cited by 37
- AlgebraicGeometry.IsZariskiLocalAtTargetproof · cited by 36
- AlgebraicGeometry.IsZariskiLocalAtTarget.mk'proof · cited by 3
- AlgebraicGeometry.IsZariskiLocalAtSource.mk'proof · cited by 2
- AlgebraicGeometry.Scheme.zariskiPrecoverage_le_fppfPrecoveragestatement · cited by 1
- AlgebraicGeometry.Scheme.zariskiPrecoverage_le_fpqcPrecoveragestatement · cited by 1
- AlgebraicGeometry.Scheme.zariskiPrecoverage_le_propQCPrecoveragestatement and proof · cited by 1
- AlgebraicGeometry.Scheme.zariskiPrecoverage_le_qcPrecoveragestatement · cited by 1
- AlgebraicGeometry.universally_isZariskiLocalAtSourceproof · cited by 0
- AlgebraicGeometry.HasAffineProperty.isZariskiLocalAtSourceproof · cited by 0
- AlgebraicGeometry.IsZariskiLocalAtSource.isZariskiLocalAtTargetproof · cited by 0
- AlgebraicGeometry.Scheme.OpenCover.exists_of_isCofiltered_of_finitestatement · cited by 0