Theorems · Definition · algebraic geometry
Module.freeLocus
(R : Type uR) → (M : Type uM) → [inst : CommRing R] → [inst_1 : AddCommGroup M] → [Module R M] → Set (PrimeSpectrum R)
The free locus of a module, i.e. the set of primes p such that Mₚ is free over Rₚ.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- Set.ofPredproof · cited by 6,101
- PrimeSpectrumstatement and proof · cited by 625
- Module.Freeproof · cited by 597
- Ideal.primeComplproof · cited by 462
- PrimeSpectrum.asIdealproof · cited by 333
- Localization.AtPrimeproof · cited by 299
- LocalizedModuleproof · cited by 154
Cited by15
Results whose statement or proof uses this declaration.
- Module.mem_freeLocus_of_isLocalizationstatement · cited by 3
- Algebra.basicOpen_subset_smoothLocus_iffproof · cited by 3
- Algebra.smoothLocus_eq_compl_support_interstatement and proof · cited by 2
- Module.basicOpen_subset_freeLocus_iffstatement and proof · cited by 2
- Algebra.isOpen_smoothLocusproof · cited by 2
- Module.freeLocus_eq_univstatement · cited by 1
- Module.freeLocus_eq_univ_iffstatement · cited by 1
- Module.freeLocus_localizationstatement and proof · cited by 1
- Module.mem_freeLocus_iff_tensorstatement · cited by 1
- Module.isLocallyConstant_rankAtStalkproof · cited by 1
- Module.isLocallyConstant_rankAtStalk_freeLocusstatement and proof · cited by 1
- Module.isOpen_freeLocusstatement and proof · cited by 1