Skip to content

feat(LocalField): instance Finite (π’ͺ[K] β§Έ 𝓂[K] ^ n) #42994

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
WenrongZou wants to merge 1 commit into
base: master
Choose a base branch
from
Open

feat(LocalField): instance Finite (π’ͺ[K] β§Έ 𝓂[K] ^ n) #42994

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
6 changes: 6 additions & 0 deletions Mathlib/NumberTheory/LocalField/Basic.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -9,6 +9,7 @@ public import Mathlib.RingTheory.Valuation.DiscreteValuativeRel
public import Mathlib.Topology.Algebra.Module.Compact
public import Mathlib.Topology.Algebra.Valued.LocallyCompact
public import Mathlib.Topology.Algebra.Valued.ValuativeRel
public import Mathlib.RingTheory.Ideal.Quotient.Index

/-!

Expand Down Expand Up @@ -36,6 +37,7 @@ This implies the following typeclasses via `inferInstance`
- `ValuativeRel.IsDiscrete K`
- `IsDiscreteValuationRing π’ͺ[K]`
- `Finite 𝓀[K]`
- `Finite (π’ͺ[K] β§Έ 𝓂[K] ^ n)`

Assuming we have a compatible `UniformSpace K` instance
(e.g. via `IsTopologicalAddGroup.toUniformSpace` and `isUniformAddGroup_of_addCommGroup`) then
Expand Down Expand Up @@ -147,6 +149,10 @@ instance : Finite 𝓀[K] :=
(compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField.mp
(inferInstanceAs (CompactSpace π’ͺ[K]))).2.2

instance (n : β„•) : Finite (π’ͺ[K] β§Έ 𝓂[K] ^ n) :=
haveI : Finite (π’ͺ[K] β§Έ 𝓂[K]) := inferInstanceAs (Finite 𝓀[K])
Ideal.finite_quotient_pow (IsNoetherian.noetherian _) n

end TopologicalSpace

section UniformSpace
Expand Down
Loading