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Theorems · Definition · commutative algebra

Algebra.Extension.toKaehler

{R : Type u} →
  {S : Type v} →
    [inst : CommRing R] →
      [inst_1 : CommRing S] → [inst_2 : Algebra R S] → (P : Algebra.Extension R S) → P.CotangentSpace →ₗ[S] Ω[S⁄R]

The projection map from the relative cotangent space to the module of differentials.

Defined in
Mathlib.RingTheory.Extension.Cotangent.Basic
Cited by
15 results in Mathlib
Foundations
Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebra

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.Generators.H1Cotangent.δ · cited by 11H1Cotangent.δAlgebra.FormallySmooth.comp_surjective · cited by 6FormallySmooth.comp_surje…Algebra.Generators.toKaehler_cotangentSpaceBasis · cited by 6Generators.toKaehler_cota…Algebra.Extension.exact_cotangentComplex_toKaehler · cited by 4Extension.exact_cotangent…Algebra.Generators.H1Cotangent.δ_eq_δAux · cited by 3H1Cotangent.δ_eq_δAuxAlgebra.Extension.toKaehler_surjective · cited by 3Extension.toKaehler_surje…Algebra.Presentation.differentials.comm₂₃ · cited by 1differentials.comm₂₃Algebra.Presentation.differentials.comm₂₃' · cited by 1differentials.comm₂₃'Algebra.Generators.H1Cotangent.δAux_ofComp · cited by 1H1Cotangent.δAux_ofCompAlgebra.Generators.H1Cotangent.δ_eq · cited by 1H1Cotangent.δ_eqAlgebra.Generators.cotangentRestrict_bijective_of_isCompl · cited by 1Generators.cotangentRestr…Algebra.Generators.disjoint_ker_toKaehler_of_linearIndependent · cited by 1Generators.disjoint_ker_t…Algebra.Generators.toKaehler_tmul_D · cited by 1Generators.toKaehler_tmul…Algebra.Generators.H1Cotangent.exact_map_δ · cited by 1H1Cotangent.exact_map_δAlgebra.Generators.H1Cotangent.exact_δ_map · cited by 1H1Cotangent.exact_δ_mapRingHom.id · cited by 18349RingHom.idCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraLinearMap · cited by 10215LinearMapKaehlerDifferential · cited by 204KaehlerDifferentialAlgebra.Extension.Ring · cited by 179Extension.RingAlgebra.Extension · cited by 138Algebra.ExtensionAlgebra.Extension.CotangentSpace · cited by 73Extension.CotangentSpaceKaehlerDifferential.mapBaseChange · cited by 12KaehlerDifferential.mapBa…Extension.toKaehlerCITED BYCITES

Cites9

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Cited by16

Results whose statement or proof uses this declaration.