feat(RingTheory): localization of Gorenstein local ring

[Thmoas-Guan]

In this PR, we proved that localization of Gorenstein local ring at prime is again Gorenstein.

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• depends on: feat(RingTheory): definition of Gorenstein local ring #31884
• depends on: [Merged by Bors] - feat(Algebra): injective dimension equal supremum of localized module #32033

[github-actions]

PR summary 2ff88851d5

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Algebra.Homology.DerivedCategory.Ext.MapBijective (new file)	1583
Mathlib.Algebra.Category.ModuleCat.Ext.Ulift (new file)	1685
Mathlib.Algebra.Category.ModuleCat.Ext.Baer (new file)	1923
Mathlib.Algebra.Category.ModuleCat.InjectiveDimension (new file)	1940
Mathlib.RingTheory.Gorenstein.Defs (new file)	1974
Mathlib.RingTheory.Gorenstein.Localization (new file)	2116

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Declarations diff

+ Functor.mapExt_bijective_of_preservesInjectiveObjects
+ Functor.mapExt_bijective_of_preservesProjectiveObjects
+ IsGorensteinLocalRing
+ IsGorensteinLocalRing.of_isLocalRing_of_isGorensteinRing
+ IsGorensteinLocalRing.of_ringEquiv
+ IsGorensteinRing
+ IsGorensteinRing.of_isGorensteinLocalRing
+ ModuleCat.extLinearEquivOfLinearEquiv
+ ModuleCat.extSemiLinearEquivOfSemiLinearEquiv
+ ModuleCat.extUliftLinearEquiv
+ ModuleCat.extUliftLinearEquiv_toLinearMap
+ ModuleCat.restrictScalars_map_exact
+ ModuleCat.shortComplexOfConj
+ ModuleCat.shortComplexOfConj_exact
+ ModuleCat.shortComplexOfConj_shortExact
+ exact_conj_of_exact
+ extRestrictScalarsSemiLinearEquiv
+ extRestrictScalarsSemiLinearMap
+ extSemiLinearEquivOfSemiLinearEquiv_equal_universe
+ ext_quotient_one_subsingleton_iff
+ hasInjectiveDimensionLE_of_quotients
+ hasInjectiveDimensionLT_of_linearEquiv
+ hasInjectiveDimensionLT_of_quotients
+ hasInjectiveDimensionLT_of_semiLinearEquiv
+ injectiveDimension_eq_of_linearEquiv
+ injectiveDimension_eq_of_semiLinearEquiv
+ injective_of_subsingleton_ext_quotient_one
+ instance : (ModuleCat.restrictScalars.{v} f).Additive
+ instance : (restrictScalars (RingHomClass.toRingHom e)).IsEquivalence
+ instance : Limits.PreservesFiniteColimits (ModuleCat.restrictScalars.{v} f) := by
+ instance : Limits.PreservesFiniteLimits (ModuleCat.restrictScalars.{v} f) := by
+ isGorensteinLocalRing_def
+ isGorensteinRing_def
+ isGorensteinRing_def'
+ isGorensteinRing_iff
+ isGorensteinRing_of_ringEquiv
+ isGoresteinLocalRing_localization
+ isGoresteinLocalRing_of_isLocalizationAtPrime
+ iso_restrictScalars

You can run this locally as follows

## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

---

Increase in tech debt: (relative, absolute) = (5.00, 0.00)

Current number	Change	Type
6420	5	backward.isDefEq.respectTransparency

Current commit 83e13bdd27
Reference commit 2ff88851d5

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• feat(RingTheory): definition of Gorenstein local ring #31884
• [Merged by Bors] - feat(Algebra): injective dimension equal supremum of localized module #32033
  By Dependent Issues (🤖). Happy coding!

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.