Theorems · Theorem · number theory
Algebra.isUnramifiedAt_bot
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [IsDomain R]
[inst_4 : IsDomain S] [Module.IsTorsionFree R S] [CharZero R] [Algebra.IsIntegral R S], Algebra.IsUnramifiedAt R ⊥In characteristic zero the generic point is unramified: if S is a domain that is integral
over a characteristic-zero domain R and R → S is injective, then S is unramified at the zero
ideal.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Fieldproof · cited by 7,404
- Idealstatement · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- CharZerostatement and proof · cited by 932
- IsFractionRingproof · cited by 738
- IsLocalizationproof · cited by 636
- Module.IsTorsionFreestatement and proof · cited by 600
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.isUnramifiedIn_botproof · cited by 0
- Algebra.isUnramifiedIn_iff_forall_of_isDedekindDomainproof · cited by 0