Theorems · Theorem · number theory
Ideal.Factors.finrank_pow_ramificationIdx
Deprecated since 2026-07-01Mathlib marks this declaration as deprecated.
∀ {R : Type u} [inst : CommRing R] {S : Type v} [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R)
[inst_3 : IsDedekindDomain S] [p.IsMaximal]
(P : ↥(UniqueFactorizationMonoid.factors (Ideal.map (algebraMap R S) p)).toFinset),
Module.finrank (R ⧸ p) (S ⧸ ↑P ^ p.ramificationIdx' ↑P) = p.ramificationIdx' ↑P * p.inertiaDeg' ↑P- Cited by
- 1 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finsetstatement · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Module.finrankstatement and proof · cited by 1,770
- Ideal.mapstatement and proof · cited by 692
- IsDedekindDomainstatement and proof · cited by 668
- Ideal.IsMaximalstatement and proof · cited by 452
- Multiset.toFinsetstatement and proof · cited by 230
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.sum_ramification_inertiaproof · cited by 4