Theorems · Definition · commutative algebra

Perfection.teichmullerFun

{p : ℕ} →
  [Fact (Nat.Prime p)] →
    {R : Type u_1} →
      [inst : CommRing R] → {I : Ideal R} → [CharP (R ⧸ I) p] → [IsPrecomplete I R] → Perfection (R ⧸ I) p → R

Given an I-adically precomplete ring R, where p ∈ I, this is the underlying function of the Teichmüller map. It is defined as the limit of p^n-th powers of arbitrary lifts in R of the n-th component from the perfection of R ⧸ I. The simp NF is teichmuller₀ when R is I-adically complete.

Defined in

Mathlib.RingTheory.Teichmuller

Cited by

4 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactCommRingCharPIsPrecomplete