Theorems · Definition · number theory

FiniteField.Extension.frob

(k : Type u_1) →
  [inst : Field k] →
    [inst_1 : Finite k] →
      (p : ℕ) →
        [inst_2 : Fact (Nat.Prime p)] →
          [inst_3 : CharP k p] → (n : ℕ) → [inst_4 : NeZero n] → Gal(FiniteField.Extension k p n/k)

The Frobenius automorphism x ↦ x ^ Nat.card k that fixes k.

Defined in: Mathlib.FieldTheory.Finite.Extension
Cited by: 4 results in Mathlib
Foundations: Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Finite Fact CharP NeZero

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Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Fieldstatement and proof · cited by 7,404
Finitestatement and proof · cited by 3,029
Factstatement and proof · cited by 2,726
Nat.Primestatement and proof · cited by 2,059
AlgEquivstatement · cited by 1,681
CharPstatement and proof · cited by 478
FiniteField.Extensionstatement and proof · cited by 13
FiniteField.frobeniusAlgEquivOfAlgebraicproof · cited by 11

Cited by4

Results whose statement or proof uses this declaration.

FiniteField.Extension.frob_applystatement · cited by 1
FiniteField.Extension.frob_iterate_applystatement and proof · cited by 1
FiniteField.exists_forall_apply_eq_powproof · cited by 1
FiniteField.Extension.exists_frob_pow_eqstatement · cited by 1