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feat: correspondence between affine group schemes and Hopf algebras#24000

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hopf_algebra_affine_group_scheme
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feat: correspondence between affine group schemes and Hopf algebras#24000
YaelDillies wants to merge 1 commit intomasterfrom
hopf_algebra_affine_group_scheme

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@YaelDillies YaelDillies commented Apr 13, 2025 •
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Construct Spec as a functor from R-Hopf algebras to group schemes over Spec R, show it is full and faithful and has affine group schemes as essential image.

From Toric, FLT

Co-authored-by: Andrew Yang the.erd.one@gmail.com
Co-authored-by: Michał Mrugała kiolterino@gmail.com
Co-authored-by: Christian Merten christian@merten.dev

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@YaelDillies @erdOne @Kiolt
feat: correspondence between Hopf algebras and affine group schemes
4134c60 
Construct `Spec` as a functor from `R`-Hopf algebras to group schemes over `Spec R`,
show it is full and faithful and has affine group schemes as essential image.

From Toric, FLT

Co-authored-by: Andrew Yang <the.erd.one@gmail.com>
Co-authored-by: Michał Mrugała <kiolterino@gmail.com>
Co-authored-by: Christian Merten
@YaelDillies YaelDillies added WIP Work in progress t-algebraic-geometry Algebraic geometry FLT part of the ongoing formalization of Fermat's Last Theorem toric Part of the ongoing formalisation of toric varieties labels Apr 13, 2025
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github-actions bot commented Apr 13, 2025

PR summary 4134c60656

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.AlgebraicGeometry.GroupScheme.HopfAffine (new file) 1992

Declarations diff

+ algSpec
+ algSpec.fullyFaithful
+ algSpec.instFaithful
+ algSpec.instFull
+ algSpec.instPreservesLimits
+ essImage_algSpec
+ essImage_hopfSpec
+ hopfSpec
+ hopfSpec.fullyFaithful
+ hopfSpec.instFaithful
+ hopfSpec.instFull

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).

kbuzzard
kbuzzard reviewed Apr 13, 2025
View reviewed changes
Mathlib/AlgebraicGeometry/GroupScheme/HopfAffine.lean
Comment on lines +7 to +10
import Toric.GroupScheme.SchemeOver
import Toric.Mathlib.Algebra.Category.CommAlg.Basic
import Toric.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Over
import Toric.Mathlib.CategoryTheory.Monoidal.Grp_
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?!

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@YaelDillies YaelDillies Apr 13, 2025

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It's WIP! Just a placeholder for the nice result to get the nice number

@YaelDillies YaelDillies changed the title feat: correspondence between Hopf algebras and affine group schemes feat: correspondence between affine group schemes and Hopf algebras Dec 10, 2025
@YaelDillies YaelDillies added blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) and removed WIP Work in progress labels Feb 1, 2026
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mathlib4-dependent-issues-bot commented Feb 1, 2026

This PR/issue depends on:

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blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) FLT part of the ongoing formalization of Fermat's Last Theorem t-algebraic-geometry Algebraic geometry toric Part of the ongoing formalisation of toric varieties

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