Theorems · Definition · algebraic geometry
Algebra.unramifiedLocus
(R : Type u_1) → (A : Type u_2) → [inst : CommRing R] → [inst_1 : CommRing A] → [Algebra R A] → Set (PrimeSpectrum A)
Algebra.unramifiedLocus R A is the set of primes p of A that are unramified.
- Defined in
- Mathlib.RingTheory.Unramified.Locus
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Quot.sound
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.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.ofPredproof · cited by 6,101
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealproof · cited by 333
- Algebra.IsUnramifiedAtproof · cited by 35
Cited by6
Results whose statement or proof uses this declaration.
- Algebra.unramifiedLocus_eq_compl_supportstatement and proof · cited by 3
- Algebra.basicOpen_subset_unramifiedLocus_iffstatement · cited by 3
- Algebra.exists_formallyUnramified_of_isUnramifiedAtproof · cited by 2
- Algebra.isOpen_unramifiedLocusstatement · cited by 2
- Algebra.unramifiedLocus_eq_univ_iffstatement · cited by 1
- Algebra.etaleLocus_eq_unramfiedLocus_inter_smoothLocusstatement · cited by 1