Theorems · Theorem · commutative algebra

WittVector.mk_pow_fontaineTheta

∀ {R : Type u} [inst : CommRing R] {p : ℕ} [inst_1 : Fact (Nat.Prime p)] [inst_2 : Fact ¬IsUnit ↑p]
  [inst_3 : IsAdicComplete (Ideal.span {↑p}) R] (n : ℕ) (x : WittVector p (PreTilt R p)),
  (Ideal.Quotient.mk (Ideal.span {↑p} ^ (n + 1))) ((WittVector.fontaineTheta R p) x) =
    (WittVector.fontaineThetaModPPow R p n) x

Defined in

Mathlib.RingTheory.Perfectoid.FontaineTheta

Cited by

2 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFactFactIsAdicComplete