Theorems · Theorem · number theory
AlgHom.IsArithFrobAt.isArithFrobAt_localize
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {φ : S →ₐ[R] S}
{Q : Ideal S} (H : φ.IsArithFrobAt Q) [inst_3 : Q.IsPrime],
H.localize.IsArithFrobAt (IsLocalRing.maximalIdeal (Localization.AtPrime Q))- Defined in
- Mathlib.RingTheory.Frobenius
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement and proof · cited by 3,236
- HasQuotient.Quotientproof · cited by 2,301
- map_mulproof · cited by 1,137
- sub_selfproof · cited by 996
- Nat.cardproof · cited by 844
- Ideal.IsPrimestatement and proof · cited by 827
- RingHomClass.toRingHomproof · cited by 746
Cited by1
Results whose statement or proof uses this declaration.
- AlgHom.IsArithFrobAt.eq_of_isUnramifiedAtproof · cited by 0