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[Merged by Bors] - feat: the prime spectrum is quasi-separated#21362

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YaelDillies wants to merge 2 commits intomasterfrom
quasi_separated_prime_spectrum
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[Merged by Bors] - feat: the prime spectrum is quasi-separated#21362
YaelDillies wants to merge 2 commits intomasterfrom
quasi_separated_prime_spectrum

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@YaelDillies YaelDillies commented Feb 3, 2025

Also golf the QuasiSeparatedSpace instance for affine schemes (the common proof was abstracted out in #21325) and prove that open sets are retrocompact iff they are compact (this should eventually become a lemma about spectral spaces).


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Also golf the `QuasiSeparatedSpace` instance for affine schemes (the common proof was abstracted out i #21325) and prove that open sets are retrocompact iff they are compact (this should eventually become a lemma about spectral spaces).
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github-actions bot commented Feb 3, 2025

PR summary 9cd466171d

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.RingTheory.Spectrum.Prime.Topology 1505 1511 +6 (+0.40%)
Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated 1871 1874 +3 (+0.16%)
Import changes for all files
Files Import difference
18 files Mathlib.AlgebraicGeometry.AffineSpace Mathlib.AlgebraicGeometry.Fiber Mathlib.AlgebraicGeometry.Morphisms.AffineAnd Mathlib.AlgebraicGeometry.Morphisms.Affine Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion Mathlib.AlgebraicGeometry.Morphisms.Finite Mathlib.AlgebraicGeometry.Morphisms.Immersion Mathlib.AlgebraicGeometry.Morphisms.Integral Mathlib.AlgebraicGeometry.Morphisms.Proper Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated Mathlib.AlgebraicGeometry.Morphisms.Separated Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed Mathlib.AlgebraicGeometry.Noetherian Mathlib.AlgebraicGeometry.PointsPi Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper Mathlib.AlgebraicGeometry.RationalMap Mathlib.AlgebraicGeometry.SpreadingOut Mathlib.AlgebraicGeometry.ValuativeCriterion
3
11 files Mathlib.AlgebraicGeometry.Morphisms.Etale Mathlib.AlgebraicGeometry.Morphisms.FiniteType Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact Mathlib.AlgebraicGeometry.Morphisms.Smooth Mathlib.AlgebraicGeometry.Sites.Etale Mathlib.RingTheory.RingHom.Unramified Mathlib.RingTheory.Smooth.Locus Mathlib.RingTheory.Spectrum.Prime.Jacobson Mathlib.RingTheory.Spectrum.Prime.Noetherian Mathlib.RingTheory.Unramified.Locus
5
48 files Mathlib.AlgebraicGeometry.AffineScheme Mathlib.AlgebraicGeometry.Cover.MorphismProperty Mathlib.AlgebraicGeometry.Cover.Open Mathlib.AlgebraicGeometry.Cover.Over Mathlib.AlgebraicGeometry.FunctionField Mathlib.AlgebraicGeometry.GammaSpecAdjunction Mathlib.AlgebraicGeometry.GluingOneHypercover Mathlib.AlgebraicGeometry.Gluing Mathlib.AlgebraicGeometry.Limits Mathlib.AlgebraicGeometry.Modules.Presheaf Mathlib.AlgebraicGeometry.Modules.Sheaf Mathlib.AlgebraicGeometry.Modules.Tilde Mathlib.AlgebraicGeometry.Morphisms.Basic Mathlib.AlgebraicGeometry.Morphisms.Constructors Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation Mathlib.AlgebraicGeometry.Morphisms.Flat Mathlib.AlgebraicGeometry.Morphisms.IsIso Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion Mathlib.AlgebraicGeometry.Morphisms.Preimmersion Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective Mathlib.AlgebraicGeometry.OpenImmersion Mathlib.AlgebraicGeometry.Over Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme Mathlib.AlgebraicGeometry.Properties Mathlib.AlgebraicGeometry.PullbackCarrier Mathlib.AlgebraicGeometry.Pullbacks Mathlib.AlgebraicGeometry.ResidueField Mathlib.AlgebraicGeometry.Restrict Mathlib.AlgebraicGeometry.Scheme Mathlib.AlgebraicGeometry.Sites.BigZariski Mathlib.AlgebraicGeometry.Sites.MorphismProperty Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski Mathlib.AlgebraicGeometry.Sites.Small Mathlib.AlgebraicGeometry.Spec Mathlib.AlgebraicGeometry.Stalk Mathlib.AlgebraicGeometry.StructureSheaf Mathlib.RingTheory.Spectrum.Maximal.Topology Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet Mathlib.RingTheory.Spectrum.Prime.FreeLocus Mathlib.RingTheory.Spectrum.Prime.IsOpenComapC Mathlib.RingTheory.Spectrum.Prime.Module Mathlib.RingTheory.Spectrum.Prime.Polynomial Mathlib.RingTheory.Spectrum.Prime.TensorProduct Mathlib.RingTheory.Spectrum.Prime.Topology
6

Declarations diff

+ instance : QuasiSeparatedSpace (PrimeSpectrum R)
+ isRetrocompact_iff
+ quasiSeparatedSpace_congr

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.


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).

@YaelDillies YaelDillies added the t-algebraic-geometry Algebraic geometry label Feb 3, 2025
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LGTM
Will wait if @alreadydone wants to take a look.

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Thanks 🎉
maintainer merge

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github-actions bot commented Feb 3, 2025

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

@github-actions github-actions bot added the maintainer-merge A reviewer has approved the changed; awaiting maintainer approval. label Feb 3, 2025
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Thanks 🎉

bors merge

@ghost ghost added ready-to-merge This PR has been sent to bors. and removed maintainer-merge A reviewer has approved the changed; awaiting maintainer approval. labels Feb 4, 2025
mathlib-bors bot pushed a commit that referenced this pull request Feb 4, 2025
Also golf the `QuasiSeparatedSpace` instance for affine schemes (the common proof was abstracted out in #21325) and prove that open sets are retrocompact iff they are compact (this should eventually become a lemma about spectral spaces).
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mathlib-bors bot commented Feb 4, 2025

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat: the prime spectrum is quasi-separated [Merged by Bors] - feat: the prime spectrum is quasi-separated Feb 4, 2025
@mathlib-bors mathlib-bors bot closed this Feb 4, 2025
@mathlib-bors mathlib-bors bot deleted the quasi_separated_prime_spectrum branch February 4, 2025 07:11
Julian added a commit that referenced this pull request Feb 5, 2025
* origin/master: (103 commits)
  chore(PresheafedSpace): remove `mk_coe` and some comments from porting  (#21382)
  refactor(CategoryTheory): `ConcreteCategory` instance for `FintypeCat` (#21466)
  refactor(Algebra/Category): clean up remaining uses of `HasForget` (#21460)
  chore(Algebra/Field/Basic): make some arguments implicit (#21453)
  chore(LinearAlgebra/TensorProduct): upgrade `TensorProduct.prodRight` (#21432)
  docs(Logic/Function/Defs): missing backticks (#21459)
  style(Logic/Embedding/Set): unindent (#21457)
  doc: document design choice of (AE)StronglyMeasurable.enorm and `edist` (#21423)
  perf(RingTheory/Artinian): reorder arguments in `IsArtinianRing.isMaximal_of_isPrime` (#21449)
  feat(Probability): first two derivatives of `cgf` (#21223)
  feat(RingTheory): `Ring.KrullDimLE` type class (#21452)
  chore(Probability/ProbabilityMassFunction/Binomial): typo "bernoulli" (#21455)
  chore: remove unused argument (#21393)
  feat(MeasureTheory/Integral/RieszMarkovKakutani) prove that the Riesz content is regular and define the Riesz measure (#20040)
  chore(Topology/Algebra/ContinuousMonoidHom): do not depend on `ContinuousLinearMap` (#21443)
  doc(CategoryTheory/Monoidal/Category): fix expression in docs (#21445)
  refactor(Order/CompleteBooleanAlgebra): a complete lattice which is a Heyting algebra is automatically a frame (#21391)
  chore: cleanup porting notes in TuringMachine (#20821)
  chore: remove @[simp] when the discr_key is a lambda (#21395)
  feat/doc: split files, add documentation (#21421)
  feat(Data/Set/Lattice): iUnion + insertion  (#21322)
  feat(Factorial): k! divides the product of any k successive integers (#21332)
  feat(CI): bench-after-CI (#21414)
  feat: primitive group actions (#12052)
  feat(Algebra/GroupWithZero/Int): add lemmas about Zm0 (#21370)
  feat(CategoryTheory): small classes of morphisms (#21411)
  feat(CategoryTheory): (co)limits of constant functors (#21412)
  chore: rename isUnit_ofPowEqOne (#21407)
  chore: split mapDomain out of MonoidAlgebra.Defs (#21398)
  chore: generalise lemmas to `ENorm` spaces, part 1 (#21380)
  chore: add `simp` to `Setoid.refl` (#21107)
  chore: tidy various files (#21406)
  chore(Geometry/Manifold/IsManifold): split out material on extended charts (#21219)
  refactor: introduce `Ideal.IsTwoSided` class for quotients of noncommutative rings (#17930)
  chore(Algebra/Category/ModuleCat): delete `ModuleCat.hasForgetModuleCat` (#21425)
  feat(RingTheory): unramified iff `κ(q)/κ(p)` is separable and `pS_q = qS_q` (#20690)
  doc(Order/Heyting/Basic): Coheyting difference is not right adjoint but left adjoint (#21418)
  chore: move ProofWidgets to v0.0.51 (#21416)
  chore: rename mem_nonZeroDivisor_of_injective and comap_nonZeroDivisor_le_of_injective (#21408)
  feat: drop ordering assumption in `RootPairing.coxeterWeight_mem_set_of_isCrystallographic` (#21122)
  feat(AlgebraicGeometry): the diagonal of an unramified morphism is an open immersion (#21386)
  feat(Data/LinearIndependent): iff versions of smul action on independent sets (#21383)
  chore(Combinatorics/SimpleGraph): Fix `hadj` naming (#21389)
  chore: rename AnalyticAt.order_neq_top_iff (#21388)
  fix: bug in daily.yml (#21401)
  chore: remove `@[simp]` from `CategoryTheory.Discrete.functor_map` (#21392)
  chore(Algebra/PUnitInstances): generalise universes (#21381)
  feat(RingTheory/PowerSeries): describe when power series map is zero (#21379)
  feat(Tactic/Linter): options to in/exclude definitions and private decls (#21374)
  feat: the prime spectrum is quasi-separated (#21362)
  ...
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