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[Merged by Bors] - feat(RingTheory/Localization/AtPrime): inertia degree and ramification index are preserved by localization#27706

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[Merged by Bors] - feat(RingTheory/Localization/AtPrime): inertia degree and ramification index are preserved by localization#27706
xroblot wants to merge 28 commits intoleanprover-community:masterfrom
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@xroblot xroblot commented Jul 30, 2025

Let R ⊆ S be an extension of rings and p be a prime ideal of R. Denote by Rₚ the localization of R at the complement of p and by Sₚ the localization of S at the (image) of the complement of p.

In this PR, we prove that the bijection between the (nonzero) prime ideals of Sₚ and the prime ideals of S above p preserves the residual degree and the ramification index.


@xroblot xroblot added the WIP Work in progress label Jul 30, 2025
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github-actions bot commented Jul 30, 2025

PR summary 665d861668

Import changes exceeding 2%

% File
+6.14% Mathlib.RingTheory.Localization.AtPrime.Extension

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.RingTheory.Localization.AtPrime.Extension 1628 1728 +100 (+6.14%)
Mathlib.NumberTheory.RamificationInertia.Basic 1726 1727 +1 (+0.06%)
Import changes for all files
Files Import difference
16 files Mathlib.NumberTheory.NumberField.AdeleRing Mathlib.NumberTheory.NumberField.ClassNumber Mathlib.NumberTheory.NumberField.DedekindZeta Mathlib.NumberTheory.NumberField.FinitePlaces Mathlib.NumberTheory.NumberField.Ideal.Asymptotics Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind Mathlib.NumberTheory.NumberField.Ideal Mathlib.NumberTheory.NumberField.ProductFormula Mathlib.NumberTheory.RamificationInertia.Basic Mathlib.NumberTheory.RamificationInertia.Galois Mathlib.NumberTheory.RamificationInertia.Unramified Mathlib.RingTheory.DedekindDomain.Different Mathlib.RingTheory.DedekindDomain.Factorization Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing Mathlib.RingTheory.DedekindDomain.LinearDisjoint Mathlib.Topology.Algebra.Ring.Compact
1
Mathlib.RingTheory.Localization.AtPrime.Extension 100

Declarations diff

+ algebraMap_equivQuotMaximalIdeal_symm_apply
+ equivQuotMaximalIdeal_apply_mk
+ equivQuotMaximalIdeal_symm_apply_mk
+ equivQuotientMapMaximalIdeal_apply_mk
+ equivQuotientMapOfIsMaximal
+ equivQuotientMapOfIsMaximal_apply_mk
+ equivQuotientMapOfIsMaximal_symm_apply_mk
+ exists_algebraMap_quot_eq_of_mem_quot
+ inertiaDeg_map_eq_inertiaDeg
+ primesOverEquivPrimesOver_inertiagDeg_eq
+ primesOverEquivPrimesOver_ramificationIdx_eq
+ ramificationIdx_bot'
+ ramificationIdx_map_eq_ramificationIdx
+ ramificationIdx_map_self_eq_one

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).

@github-actions github-actions bot added the file-removed A Lean module was (re)moved without a `deprecated_module` annotation label Jul 30, 2025
@xroblot xroblot changed the title feat(RingTheory/Localization/AtPrime): Add results about primes in extension feat(RingTheory/Localization/AtPrime): Add results about prime ideals in extension Aug 1, 2025
@xroblot xroblot removed the WIP Work in progress label Aug 1, 2025
@mathlib4-dependent-issues-bot mathlib4-dependent-issues-bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Aug 1, 2025
@mathlib4-merge-conflict-bot mathlib4-merge-conflict-bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Aug 1, 2025
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This pull request has conflicts, please merge master and resolve them.

@github-actions github-actions bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Aug 2, 2025
mathlib-bors bot pushed a commit that referenced this pull request Aug 3, 2025
…lization/AtPrime/Basic.lean` (#27795)

Create the directory `Mathlib/RingTheory/Localization/AtPrime` and move the file `Mathlib/RingTheory/Localization/AtPrime.lean` to `Mathlib/RingTheory/Localization/AtPrime/Basic.lean`. 

This is needed to make way for the new file `Mathlib/RingTheory/Localization/AtPrime/Extension.lean` in #27706 since the results of this file cannot be added to the file `Mathlib/RingTheory/Localization/AtPrime.lean` because of circular dependencies. 

The deprecated module is added in the following PR: #27796
@mathlib4-merge-conflict-bot mathlib4-merge-conflict-bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Aug 3, 2025
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This pull request has conflicts, please merge master and resolve them.

@grunweg grunweg added the t-ring-theory Ring theory label Aug 4, 2025
Equilibris pushed a commit to Equilibris/mathlib4 that referenced this pull request Aug 7, 2025
…lization/AtPrime/Basic.lean` (leanprover-community#27795)

Create the directory `Mathlib/RingTheory/Localization/AtPrime` and move the file `Mathlib/RingTheory/Localization/AtPrime.lean` to `Mathlib/RingTheory/Localization/AtPrime/Basic.lean`. 

This is needed to make way for the new file `Mathlib/RingTheory/Localization/AtPrime/Extension.lean` in leanprover-community#27706 since the results of this file cannot be added to the file `Mathlib/RingTheory/Localization/AtPrime.lean` because of circular dependencies. 

The deprecated module is added in the following PR: leanprover-community#27796
@xroblot xroblot added the WIP Work in progress label Aug 11, 2025
@mathlib4-dependent-issues-bot mathlib4-dependent-issues-bot removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Aug 12, 2025
@xroblot xroblot added the WIP Work in progress label Nov 24, 2025
@mathlib4-dependent-issues-bot mathlib4-dependent-issues-bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Nov 27, 2025
@xroblot xroblot removed the WIP Work in progress label Dec 2, 2025
@mathlib4-dependent-issues-bot mathlib4-dependent-issues-bot removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Dec 13, 2025
@erdOne erdOne added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Dec 13, 2025
@riccardobrasca riccardobrasca self-assigned this Dec 15, 2025
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Can you please fix the conflict?

@github-actions github-actions bot added large-import Automatically added label for PRs with a significant increase in transitive imports and removed merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) labels Dec 15, 2025
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xroblot commented Dec 15, 2025

Can you please fix the conflict?

Yes, but I want to have another look at this one since many things have changed so I'll tag it WIP for the time being.

@xroblot xroblot added the WIP Work in progress label Dec 15, 2025
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xroblot commented Jan 4, 2026

Can you please fix the conflict?

Yes, but I want to have another look at this one since many things have changed so I'll tag it WIP for the time being.

Well, I guess I cannot really improve it much so I'll remove the WIP tag and this PR is open for review.

@xroblot xroblot removed the WIP Work in progress label Jan 4, 2026
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Thanks!

bors merge


-- Lean thinks that the instance [p.IsPrime] is not necessary here, but it is needed
-- for the definition of `Rₚ`.
set_option linter.unusedSectionVars false in
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Can you ask on Zulip if it is worth to open an issue here?

@ghost ghost added the ready-to-merge This PR has been sent to bors. label Jan 11, 2026
mathlib-bors bot pushed a commit that referenced this pull request Jan 11, 2026
…n index are preserved by localization (#27706)

Let `R ⊆ S` be an extension of rings and `p` be a prime ideal of `R`. Denote by `Rₚ` the localization of `R` at the complement of `p` and by `Sₚ` the localization of `S` at the (image) of the complement of `p`.

In this PR, we prove that the bijection between the (nonzero) prime ideals of `Sₚ` and the prime ideals of `S` above `p` preserves the residual degree and the ramification index.
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mathlib-bors bot commented Jan 11, 2026

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(RingTheory/Localization/AtPrime): inertia degree and ramification index are preserved by localization [Merged by Bors] - feat(RingTheory/Localization/AtPrime): inertia degree and ramification index are preserved by localization Jan 11, 2026
@mathlib-bors mathlib-bors bot closed this Jan 11, 2026
@adomani adomani mentioned this pull request Jan 16, 2026
eliasjudin pushed a commit to eliasjudin/mathlib4 that referenced this pull request Jan 18, 2026
…n index are preserved by localization (leanprover-community#27706)

Let `R ⊆ S` be an extension of rings and `p` be a prime ideal of `R`. Denote by `Rₚ` the localization of `R` at the complement of `p` and by `Sₚ` the localization of `S` at the (image) of the complement of `p`.

In this PR, we prove that the bijection between the (nonzero) prime ideals of `Sₚ` and the prime ideals of `S` above `p` preserves the residual degree and the ramification index.
goliath-klein pushed a commit to PrParadoxy/mathlib4 that referenced this pull request Jan 24, 2026
…n index are preserved by localization (leanprover-community#27706)

Let `R ⊆ S` be an extension of rings and `p` be a prime ideal of `R`. Denote by `Rₚ` the localization of `R` at the complement of `p` and by `Sₚ` the localization of `S` at the (image) of the complement of `p`.

In this PR, we prove that the bijection between the (nonzero) prime ideals of `Sₚ` and the prime ideals of `S` above `p` preserves the residual degree and the ramification index.
@xroblot xroblot deleted the locatprime_ext branch March 16, 2026 15:31
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6 participants