Theorems · Theorem · algebraic geometry
Module.rankAtStalk_eq_of_le_of_finite_of_flat
∀ {R : Type uR} (M : Type uM) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Flat R M]
[Module.Finite R M] {p q : PrimeSpectrum R}, p ≤ q → Module.rankAtStalk M p = Module.rankAtStalk M q- Cited by
- 1 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebra.algebraMapproof · cited by 4,706
- Module.finrankproof · cited by 1,770
- Module.Finitestatement and proof · cited by 1,032
- PrimeSpectrumstatement and proof · cited by 625
- Ideal.primeComplproof · cited by 462
- PrimeSpectrum.asIdealproof · cited by 333
- Localization.AtPrimeproof · cited by 299
- Module.Flatstatement and proof · cited by 279
Cited by1
Results whose statement or proof uses this declaration.
- Module.rankAtStalk_eq_of_le_of_finite_of_flat'proof · cited by 1