Theorems · Theorem · algebraic geometry

PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal

∀ (R : Type u_3) (S : Type u_4) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R)
  [inst_3 : p.IsPrime] (a : ↑(p.primesOver S)),
  ↑((PrimeSpectrum.primesOverOrderIsoFiber R S p) a).asIdeal =
    ⇑(Algebra.TensorProduct.lift (Ideal.ResidueField.mapₐ p (↑a) (Algebra.ofId R S) ⋯)
          (IsScalarTower.toAlgHom R S (↑a).ResidueField) ⋯) ⁻¹'
      {0}

Defined in: Mathlib.RingTheory.LocalRing.ResidueField.Fiber
Cited by: 1 results in Mathlib
Foundations: Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra Ideal.IsPrime

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Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_topproof · cited by 1