feat(RingTheory/Homology): `Ext` over Noetherian ring finitely generated

[Thmoas-Guan]

In this PR, we proved that for Ext between finitely generated modules over Noetherian ring finitely generated.

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• [ ] depends on: #32316

[github-actions[bot]]

PR summary 86622378a5

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Algebra.Category.ModuleCat.Ext.DimensionShifting (new file)	1717
Mathlib.Algebra.Category.ModuleCat.Ext.Finite (new file)	1718

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Declarations diff

+ CategoryTheory.InjectivePresentation.shortComplex + CategoryTheory.InjectivePresentation.shortComplex_shortExact + LinearMap.shortComplexKer + LinearMap.shortExact_shortComplexKer + Module.exists_finite_presentation + Module.finite_shrink + Module.free_shrink + ModuleCat.finite_ext + ModuleCat.projective_shortComplex + ModuleCat.projective_shortComplex_shortExact + extClass_postcomp_surjective_of_projective_X₂ + extClass_precomp_surjective_of_projective_X₂ + instance [Small.{v} R] (M : ModuleCat.{v} R) : Module.Free R M.projective_shortComplex.X₂ + instance {M : ModuleCat.{v} R} (ip : InjectivePresentation M) : Injective ip.shortComplex.X₂ := ip.2 + subsingleton_of_injective + subsingleton_of_projective

You can run this locally as follows

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

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

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

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No changes to technical debt.

You can run this locally as

./scripts/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:

• leanprover-community/mathlib4#32316 By Dependent Issues (🤖). Happy coding!

[mathlib4-merge-conflict-bot]

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