[Merged by Bors] - feat(RingTheory): smooth algebras have smooth Noetherian models

[chrisflav]

Co-authored by: Judith Ludwig ludwig@mathi.uni-heidelberg.de

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• depends on: [Merged by Bors] - feat(RingTheory/Presentation): core of a presentation #24794

[github-actions]

PR summary 920783b3b4

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.RingTheory.MvPolynomial.Homogeneous	996	1008	+12 (+1.20%)

Import changes for all files

Files	Import difference
6 files Mathlib.Algebra.Lie.CartanExists Mathlib.Algebra.Lie.Rank Mathlib.Algebra.Module.LinearMap.Polynomial Mathlib.Algebra.MvPolynomial.Nilpotent Mathlib.Combinatorics.Nullstellensatz Mathlib.LinearAlgebra.Matrix.Charpoly.Univ	1
Mathlib.RingTheory.MvPolynomial.Ideal	5
3 files Mathlib.RingTheory.MvPolynomial.Groebner Mathlib.RingTheory.MvPolynomial.MonomialOrder.DegLex Mathlib.RingTheory.MvPolynomial.MonomialOrder	11
3 files Mathlib.Algebra.Polynomial.Homogenize Mathlib.RingTheory.MvPolynomial.EulerIdentity Mathlib.RingTheory.MvPolynomial.Homogeneous	12
Mathlib.RingTheory.Smooth.NoetherianDescent (new file)	1472

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Declarations diff

+ C_mul
+ DescentAux
+ Ideal.mem_span_iff_exists_isHomogeneous
+ Ideal.mem_span_pow_iff_exists_isHomogeneous
+ Ideal.span_eq_map_homogeneousSubmodule
+ Ideal.span_pow_eq_map_homogeneousSubmodule
+ _root_.AlgHom.kerSquareLift_mk
+ algebra₀
+ algebra₁
+ algebra₂
+ coeffs_h_subset
+ coeffs_p_subset
+ coeffs_q_subset
+ eval₂_map_comp_C
+ exists_kerSquareLift_comp_eq_id
+ hasCoeffs
+ homogeneousSubmodule_one_eq_span_X
+ homogeneousSubmodule_one_pow
+ homogeneousSubmodule_zero
+ induction_on
+ instance : CommRing (D.subalgebra R) := inferInstanceAs <| CommRing (Algebra.adjoin _ _)
+ instance : FaithfulSMul (D.subalgebra R) A := inferInstanceAs <| FaithfulSMul (Algebra.adjoin _ _) _
+ instance : IsScalarTower (D.subalgebra R) A B
+ instance [Finite D.vars] [Finite D.rels] : Algebra.FiniteType R (D.subalgebra R) := by
+ map_eval
+ monomial_mem_homogeneousSubmodule_pow_degree
+ of_map
+ range_single_one
+ subalgebra

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).

[leanprover-community-bot-assistant]

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

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - feat(RingTheory/Presentation): core of a presentation #24794
  By Dependent Issues (🤖). Happy coding!

[erdOne]

Thanks!
maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by erdOne.

[jcommelin]

Thanks 🎉

bors d+

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✌️ chrisflav can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[chrisflav]

Thanks for the reviews!

bors r+

[mathlib-bors]

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[chrisflav]

bors r-

[chrisflav]

bors r+

[mathlib-bors]

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