feat(Algebra): finite projective dimension of regular - #29557
feat(Algebra): finite projective dimension of regular#29557Thmoas-Guan wants to merge 2853 commits into
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| Files | Import difference |
|---|---|
Mathlib.RingTheory.RegularLocalRing.Basic (new file) |
2226 |
Mathlib.RingTheory.Depth.Basic (new file) |
2333 |
Mathlib.RingTheory.Depth.Ischebeck (new file) |
2369 |
Mathlib.RingTheory.Depth.AuslanderBuchsbaum (new file) |
2419 |
Mathlib.RingTheory.CohenMacaulay.Basic (new file) |
2474 |
Mathlib.RingTheory.CohenMacaulay.Maximal (new file) |
2487 |
Mathlib.RingTheory.RegularLocalRing.GlobalDimension (new file) |
2495 |
Declarations diff (regex)
+ AuslanderBuchsbaum
+ AuslanderBuchsbaum_one
+ FiniteRingKrullDim.ringKrullDim_eq_nat
+ Ideal.depth
+ Ideal.depth_eq_of_iso
+ Ideal.depth_eq_of_linearEquiv
+ Ideal.depth_eq_top_of_subsingleton
+ Ideal.depth_quotSMulTop_succ_eq_moduleDepth
+ Ideal.span_singleton_mul_eq_self_of_isPrime
+ IsCohenMacaulayLocalRing
+ IsCohenMacaulayLocalRing.of_isLocalRing_of_isCohenMacaulayRing
+ IsCohenMacaulayRing
+ IsCohenMacaulayRing.of_isCohenMacaulayLocalRing
+ IsDiscreteValuationRing.of_isRegularLocalRing_of_ringKrullDim_eq_one
+ IsLocalRing.depth
+ IsLocalRing.depth_eq_of_algebraMap_surjective
+ IsLocalRing.depth_eq_of_iso
+ IsLocalRing.depth_eq_of_linearEquiv
+ IsLocalRing.depth_eq_of_ringEquiv
+ IsLocalRing.depth_eq_sSup_length_regular
+ IsLocalRing.depth_eq_top_of_subsingleton
+ IsLocalRing.depth_quotSMulTop_succ_eq_moduleDepth
+ IsLocalRing.depth_quotient_regular_sequence_add_length_eq_depth
+ IsLocalRing.depth_quotient_regular_succ_eq_depth
+ IsLocalRing.depth_quotient_span_regular_succ_eq_depth
+ IsLocalRing.ideal_depth_eq_sSup_length_regular
+ IsLocalRing.ideal_depth_le_depth
+ IsLocalRing.spanFinrank_maximalIdeal_add_finrank_eq_of_surjective
+ IsLocalRing.spanFinrank_maximalIdeal_quotient
+ LinearMapOfSemiLinearMapAlgebraMap
+ ModuleCat.IsCohenMacaulay
+ ModuleCat.IsCohenMacaulay_of_iso
+ ModuleCat.IsMaximalCohenMacaulay
+ ModuleCat.depth_eq_supportDim_of_cohenMacaulay
+ ModuleCat.depth_eq_supportDim_unbot_of_cohenMacaulay
+ ModuleCat.free_of_projective_of_isLocalRing
+ ModuleCat.isCohenMacaulay_iff
+ SemiLinearMapAlgebraMapOfLinearMap
+ Submodule.comap_lt_top_of_lt_range
+ associatedPrimes_self_eq_minimalPrimes
+ associated_prime_eq_minimalPrimes_isCohenMacaulay
+ associated_prime_minimal_of_isCohenMacaulay
+ basis_lift
+ basis_lift_ker_le
+ depth_eq_dim_quotient_associated_prime_of_isCohenMacaulay
+ depth_le_ringKrullDim
+ depth_le_ringKrullDim_associatedPrime
+ depth_le_supportDim
+ depth_ne_top
+ depth_quotient_regular_sequence_add_length_eq_depth
+ ext_hom_zero_of_mem_ideal_smul
+ ext_subsingleton_of_lt_moduleDepth
+ finite_projectiveDimension_of_isRegularLocalRing_aux
+ finte_free_ext_vanish_iff
+ free_depth_eq_ring_depth
+ free_of_isMaximalCohenMacaulay_of_isRegularLocalRing
+ ideal_depth_quotient_regular_sequence_add_length_eq_ideal_depth
+ instance (I : Ideal R) (M : Type*) [AddCommGroup M] [Module R M]
+ instance (R : Type*) [CommRing R] (I : Ideal R) [IsNoetherianRing R] :
+ instance (priority := low) [IsNoetherianRing R] [IsLocalRing R] [Small.{v} R]
+ instance : RingHomSurjective (residue R) := ⟨residue_surjective⟩
+ instance [IsCohenMacaulayLocalRing R] : (ModuleCat.of R R).IsCohenMacaulay
+ instance [IsRegularLocalRing R] : IsDomain R := isDomain_of_isRegularLocalRing R
+ isCohenMacaulayLocalRing_def
+ isCohenMacaulayLocalRing_iff
+ isCohenMacaulayLocalRing_localization_atPrime
+ isCohenMacaulayLocalRing_of_isRegularLocalRing
+ isCohenMacaulayLocalRing_of_ringEquiv
+ isCohenMacaulayLocalRing_of_ringKrullDim_le_depth
+ isCohenMacaulayRing_def
+ isCohenMacaulayRing_def'
+ isCohenMacaulayRing_iff
+ isCohenMacaulayRing_of_ringEquiv
+ isCohenMacaulay_of_isMaximalCohenMacaulay
+ isDomain_of_isRegularLocalRing
+ isField_of_isRegularLocalRing_of_dimension_zero
+ isLocalization_at_prime_prime_depth_le_depth
+ isLocalize_at_prime_depth_eq_of_isCohenMacaulay
+ isLocalize_at_prime_dim_eq_prime_depth_of_isCohenMacaulay
+ isLocalize_at_prime_isCohenMacaulay_of_isCohenMacaulay
+ isLocalizedModule_quotSMulTopIsLocalizedModuleMap
+ isMaximalCohenMacaulay_def
+ isRegular_of_span_eq_maximalIdeal
+ mem_smul_top_of_range_le_smul_top
+ moduleDepth
+ moduleDepth_eq_depth_of_supp_eq
+ moduleDepth_eq_find
+ moduleDepth_eq_iff
+ moduleDepth_eq_of_iso_fst
+ moduleDepth_eq_of_iso_snd
+ moduleDepth_eq_of_linearEquiv
+ moduleDepth_eq_sSup_length_regular
+ moduleDepth_eq_sup_nat
+ moduleDepth_eq_top_iff
+ moduleDepth_eq_zero_of_hom_nontrivial
+ moduleDepth_ge_depth_sub_dim
+ moduleDepth_ge_min_of_shortExact_fst_fst
+ moduleDepth_ge_min_of_shortExact_fst_snd
+ moduleDepth_ge_min_of_shortExact_snd_fst
+ moduleDepth_ge_min_of_shortExact_snd_snd
+ moduleDepth_ge_min_of_shortExact_trd_fst
+ moduleDepth_ge_min_of_shortExact_trd_snd
+ moduleDepth_lt_top_iff
+ moduleDepth_quotSMulTop_succ_eq_moduleDepth
+ moduleDepth_quotient_regular_sequence_add_length_eq_moduleDepth
+ nontrivial_ring_of_nontrivial_module
+ projectiveDimension_ne_top_of_isRegularLocalRing
+ quotSMulTopIsLocalizedModuleMap
+ quotSMulTop_isCohenMacaulay_iff_isCohenMacaulay
+ quotient_isRegularLocalRing_tfae
+ quotient_prime_ringKrullDim_ne_bot
+ quotient_regular_isCohenMacaulay_iff_isCohenMacaulay
+ quotient_regular_sequence_isCohenMacaulay_iff_isCohenMacaulay
+ quotient_regular_smul_top_isCohenMacaulay_iff_isCohenMacaulay
+ quotient_span_regular_isCohenMacaulay_iff_isCohenMacaulay
+ quotient_span_singleton
+ ring_depth_shrink_eq
+ smul_prod_of_smul
+ subsingleton_of_pi
+ toCotangentSpace
You can run this locally as follows
## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>
## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.
Declarations diff (Lean)
✅ Lean-aware diff — post-build, computed from the Lean environment (commit
c659a4f).
- +146 new declarations
- −0 removed declarations
+AuslanderBuchsbaum
+AuslanderBuchsbaum_one
+FiniteRingKrullDim.ringKrullDim_eq_nat
+Ideal.depth
+Ideal.depth.congr_simp
+Ideal.depth_eq_of_iso
+Ideal.depth_eq_of_linearEquiv
+Ideal.depth_eq_top_of_subsingleton
+Ideal.depth_quotSMulTop_succ_eq_moduleDepth
+Ideal.span_singleton_mul_eq_self_of_isPrime
+IsCohenMacaulayLocalRing
+IsCohenMacaulayLocalRing.casesOn
+IsCohenMacaulayLocalRing.depth_eq_dim
+IsCohenMacaulayLocalRing.mk
+IsCohenMacaulayLocalRing.of_isLocalRing_of_isCohenMacaulayRing
+IsCohenMacaulayLocalRing.rec
+IsCohenMacaulayLocalRing.recOn
+IsCohenMacaulayLocalRing.toIsLocalRing
+IsCohenMacaulayRing
+IsCohenMacaulayRing.CM_localize
+IsCohenMacaulayRing.casesOn
+IsCohenMacaulayRing.mk
+IsCohenMacaulayRing.of_isCohenMacaulayLocalRing
+IsCohenMacaulayRing.rec
+IsCohenMacaulayRing.recOn
+IsDiscreteValuationRing.of_isRegularLocalRing_of_ringKrullDim_eq_one
+IsLocalRing.CotangentSpace.congr_simp
+IsLocalRing.depth
+IsLocalRing.depth.congr_simp
+IsLocalRing.depth_eq_of_algebraMap_surjective
+IsLocalRing.depth_eq_of_iso
+IsLocalRing.depth_eq_of_linearEquiv
+IsLocalRing.depth_eq_of_ringEquiv
+IsLocalRing.depth_eq_sSup_length_regular
+IsLocalRing.depth_eq_top_of_subsingleton
+IsLocalRing.depth_quotSMulTop_succ_eq_moduleDepth
+IsLocalRing.depth_quotient_regular_sequence_add_length_eq_depth
+IsLocalRing.depth_quotient_regular_succ_eq_depth
+IsLocalRing.depth_quotient_span_regular_succ_eq_depth
+IsLocalRing.ideal_depth_eq_sSup_length_regular
+IsLocalRing.ideal_depth_le_depth
+IsLocalRing.instRingHomSurjectiveResidueFieldResidue
+IsLocalRing.spanFinrank_maximalIdeal_add_finrank_eq_of_surjective
+IsLocalRing.spanFinrank_maximalIdeal_quotient
+IsLocalRing.toCotangentSpace
+LinearMapOfSemiLinearMapAlgebraMap
+ModuleCat.IsCohenMacaulay
+ModuleCat.IsCohenMacaulay.casesOn
+ModuleCat.IsCohenMacaulay.congr_simp
+ModuleCat.IsCohenMacaulay.depth_eq_dim
+ModuleCat.IsCohenMacaulay.mk
+ModuleCat.IsCohenMacaulay.rec
+ModuleCat.IsCohenMacaulay.recOn
+ModuleCat.IsCohenMacaulay_of_iso
+ModuleCat.IsMaximalCohenMacaulay
+ModuleCat.IsMaximalCohenMacaulay.casesOn
+ModuleCat.IsMaximalCohenMacaulay.depth_eq_dim
+ModuleCat.IsMaximalCohenMacaulay.mk
+ModuleCat.IsMaximalCohenMacaulay.rec
+ModuleCat.IsMaximalCohenMacaulay.recOn
+ModuleCat.depth_eq_supportDim_of_cohenMacaulay
+ModuleCat.depth_eq_supportDim_unbot_of_cohenMacaulay
+ModuleCat.free_of_projective_of_isLocalRing
+ModuleCat.isCohenMacaulay_iff
+SemiLinearMapAlgebraMapOfLinearMap
+SemiLinearMapAlgebraMapOfLinearMap.congr_simp
+Submodule.comap_lt_top_of_lt_range
+associatedPrimes_self_eq_minimalPrimes
+associated_prime_eq_minimalPrimes_isCohenMacaulay
+associated_prime_minimal_of_isCohenMacaulay
+basis_lift
+basis_lift_ker_le
+depth_eq_dim_quotient_associated_prime_of_isCohenMacaulay
+depth_le_ringKrullDim
+depth_le_ringKrullDim_associatedPrime
+depth_le_supportDim
+depth_ne_top
+depth_quotient_regular_sequence_add_length_eq_depth
+ext_hom_zero_of_mem_ideal_smul
+ext_subsingleton_of_lt_moduleDepth
+finite_projectiveDimension_of_isRegularLocalRing_aux
+finte_free_ext_vanish_iff
+free_depth_eq_ring_depth
+free_of_isMaximalCohenMacaulay_of_isRegularLocalRing
+ideal_depth_quotient_regular_sequence_add_length_eq_ideal_depth
+instFiniteQuotientIdealSubmoduleHSMulTop
+instIsCohenMacaulayOf
+instIsDomainOfIsRegularLocalRing
+instNontrivialCarrierOfIsNoetherianRingOfIsMaximalCohenMacaulay
+isCohenMacaulayLocalRing_def
+isCohenMacaulayLocalRing_iff
+isCohenMacaulayLocalRing_localization_atPrime
+isCohenMacaulayLocalRing_of_isRegularLocalRing
+isCohenMacaulayLocalRing_of_ringEquiv
+isCohenMacaulayLocalRing_of_ringKrullDim_le_depth
+isCohenMacaulayRing_def
+isCohenMacaulayRing_def'
+isCohenMacaulayRing_iff
+isCohenMacaulayRing_of_ringEquiv
+isCohenMacaulay_of_isMaximalCohenMacaulay
+isDomain_of_isRegularLocalRing
+isField_of_isRegularLocalRing_of_dimension_zero
+isLocalization_at_prime_prime_depth_le_depth
+isLocalize_at_prime_depth_eq_of_isCohenMacaulay
+isLocalize_at_prime_dim_eq_prime_depth_of_isCohenMacaulay
+isLocalize_at_prime_isCohenMacaulay_of_isCohenMacaulay
+isLocalizedModule_quotSMulTopIsLocalizedModuleMap
+isMaximalCohenMacaulay_def
+isRegular_of_span_eq_maximalIdeal
+mem_smul_top_of_range_le_smul_top
+moduleDepth
+moduleDepth.congr_simp
+moduleDepth_eq_depth_of_supp_eq
+moduleDepth_eq_find
+moduleDepth_eq_iff
+moduleDepth_eq_of_iso_fst
+moduleDepth_eq_of_iso_snd
+moduleDepth_eq_of_linearEquiv
+moduleDepth_eq_sSup_length_regular
+moduleDepth_eq_sup_nat
+moduleDepth_eq_top_iff
+moduleDepth_eq_zero_of_hom_nontrivial
+moduleDepth_ge_depth_sub_dim
+moduleDepth_ge_min_of_shortExact_fst_fst
+moduleDepth_ge_min_of_shortExact_fst_snd
+moduleDepth_ge_min_of_shortExact_snd_fst
+moduleDepth_ge_min_of_shortExact_snd_snd
+moduleDepth_ge_min_of_shortExact_trd_fst
+moduleDepth_ge_min_of_shortExact_trd_snd
+moduleDepth_lt_top_iff
+moduleDepth_quotSMulTop_succ_eq_moduleDepth
+moduleDepth_quotient_regular_sequence_add_length_eq_moduleDepth
+nontrivial_ring_of_nontrivial_module
+projectiveDimension_ne_top_of_isRegularLocalRing
+quotSMulTopIsLocalizedModuleMap
+quotSMulTop_isCohenMacaulay_iff_isCohenMacaulay
+quotient_isRegularLocalRing_tfae
+quotient_prime_ringKrullDim_ne_bot
+quotient_regular_isCohenMacaulay_iff_isCohenMacaulay
+quotient_regular_sequence_isCohenMacaulay_iff_isCohenMacaulay
+quotient_regular_smul_top_isCohenMacaulay_iff_isCohenMacaulay
+quotient_span_regular_isCohenMacaulay_iff_isCohenMacaulay
+quotient_span_singleton
+ring_depth_shrink_eq
+smul_prod_of_smul
+subsingleton_of_piIncrease in strong tech debt: (relative, absolute) = (7.00, 0.00)
| Current number | Change | Type (strong) |
|---|---|---|
| 6994 | 7 | backward.isDefEq.respectTransparency |
Increase in weak tech debt: (relative, absolute) = (5.00, 0.00)
| Current number | Change | Type (weak) |
|---|---|---|
| 5052 | 5 | exposed public sections |
Current commit c659a4f59a
Reference commit 9c0c555bde
This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary
- The
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
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4 participants
In this PR, we proved every finitely generated module over regular local ring has finite projective dimension. With this and Auslander Buchsbaum theorem, we can obtain the global dimension of regular local ring is equal to its krull dimension.