Theorems · Definition · number theory

WittVector.IsocrystalEquiv.casesOn

{p : ℕ} →
  [inst : Fact (Nat.Prime p)] →
    {k : Type u_1} →
      [inst_1 : CommRing k] →
        [inst_2 : CharP k p] →
          [inst_3 : PerfectRing k p] →
            {V : Type u_2} →
              [inst_4 : AddCommGroup V] →
                [inst_5 : WittVector.Isocrystal p k V] →
                  {V₂ : Type u_3} →
                    [inst_6 : AddCommGroup V₂] →
                      [inst_7 : WittVector.Isocrystal p k V₂] →
                        {motive : WittVector.IsocrystalEquiv p k V V₂ → Sort u} →
                          (t : WittVector.IsocrystalEquiv p k V V₂) →
                            ((toLinearEquiv : V ≃ₗ[FractionRing (WittVector p k)] V₂) →
                                (frob_equivariant :
                                    ∀ (x : V),
                                      (WittVector.Isocrystal.frobenius p k) (toLinearEquiv x) =
                                        toLinearEquiv ((WittVector.Isocrystal.frobenius p k) x)) →
                                  motive { toLinearEquiv := toLinearEquiv, frob_equivariant := frob_equivariant }) →
                              motive t

Defined in

Mathlib.RingTheory.WittVector.Isocrystal

Cited by

0 results in Mathlib

Foundations

Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactCommRingCharPPerfectRingAddCommGroupWittVector.IsocrystalAddCommGroupWittVector.Isocrystal