Theorems · Definition · algebraic geometry
AlgebraicGeometry.StructureSheaf.commRingCatStalkEquivModuleStalk
(R : Type u) →
[inst : CommRing R] →
(x : ↑(AlgebraicGeometry.PrimeSpectrum.Top R)) →
↑(TopCat.Presheaf.stalk (AlgebraicGeometry.moduleStructurePresheaf R R).presheaf x) ≃ₗ[R]
↑((AlgebraicGeometry.structurePresheafInCommRingCat R).stalk x)The stalk of Spec R at x is isomorphic to the stalk of R^~ at x.
- Defined in
- Mathlib.AlgebraicGeometry.StructureSheaf
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
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Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Oppositestatement · cited by 8,081
- CategoryTheory.Functor.compstatement and proof · cited by 6,529
- LinearEquivstatement · cited by 3,317
- TopCat.carrierstatement and proof · cited by 3,184
- CommRingCatstatement and proof · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- CategoryTheory.Limits.Cocone.ptproof · cited by 1,354
- CommRingCat.carrierstatement · cited by 1,096
- AddEquivproof · cited by 1,087
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