Theorems · Theorem · commutative algebra
Ideal.inertiaDeg_eq
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R)
(q : Ideal S) [inst_3 : q.LiesOver p] [inst_4 : q.IsPrime] [inst_5 : p.IsPrime]
[inst_6 : Algebra (Localization.AtPrime p) (Localization.AtPrime q)]
[inst_7 : Localization.AtPrime.IsLiesOverAlgebra p q], q.inertiaDeg R = Module.finrank p.ResidueField q.ResidueField- Cited by
- 6 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Algebrastatement and proof · cited by 11,388
- Idealstatement and proof · cited by 4,748
- Module.finrankstatement · cited by 1,770
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplstatement · cited by 462
- Localization.AtPrimestatement and proof · cited by 299
- Ideal.LiesOverstatement and proof · cited by 272
- Ideal.underproof · cited by 170
- Ideal.ResidueFieldstatement · cited by 119
- Ideal.inertiaDegstatement · cited by 60
- Ideal.over_defproof · cited by 60
Cited by6
Results whose statement or proof uses this declaration.
- Ideal.inertiaDeg_towerproof · cited by 7
- Ideal.inertiaDeg_smulproof · cited by 2
- Ideal.card_stabilizer_eq_card_inertia_mul_finrankproof · cited by 2
- Ideal.inertiaDeg_eq_of_isFractionRingproof · cited by 2
- Ideal.sum_ramification_inertia_eq_finrank_fiberproof · cited by 1
- Ideal.inertiaDeg'_eqproof · cited by 0