Theorems · Definition · algebraic geometry
AlgebraicGeometry.AlgebraicCycle
AlgebraicGeometry.Scheme → (R : Type u_2) → [Zero R] → Type (max u u_2)
Algebraic cycle on a scheme X with coefficients in a type Z is just a function from X to Z
with locally finite support (see the module docstring for more details).
Note: currently this is an abbrev to save some effort in duplicating API. This seems fine for now,
but be aware of this if there is ever an instance clash involving algebraic cycles.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- Zero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- Function.locallyFinsuppproof · cited by 43
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.AlgebraicCycle.mapstatement and proof · cited by 1
- AlgebraicGeometry.AlgebraicCycle.map_idstatement and proof · cited by 0