Skip to content
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

finish adicCompletionTensorComapContinuousAlgHom #251

Merged
merged 1 commit into from
Dec 1, 2024
Merged

finish adicCompletionTensorComapContinuousAlgHom #251

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
13 changes: 12 additions & 1 deletion FLT/DedekindDomain/FiniteAdeleRing/BaseChange.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -277,11 +277,22 @@ attribute [local instance] Algebra.TensorProduct.rightAlgebra in
variable (v : HeightOneSpectrum A) in
instance : TopologicalSpace (L ⊗[K] adicCompletion K v) := moduleTopology (adicCompletion K v) _

attribute [local instance] Algebra.TensorProduct.rightAlgebra in
variable (v : HeightOneSpectrum A) in
instance : IsModuleTopology (adicCompletion K v) (L ⊗[K] adicCompletion K v) :=
⟨rfl⟩

attribute [local instance] Algebra.TensorProduct.rightAlgebra in
noncomputable def adicCompletionTensorComapContinuousAlgHom (v : HeightOneSpectrum A) :
L ⊗[K] adicCompletion K v →A[L]
Π w : {w : HeightOneSpectrum B // v = comap A w}, adicCompletion L w.1 where
__ := adicCompletionTensorComapAlgHom A K L B v
cont := sorry -- #237
cont := by
apply IsModuleTopology.continuous_of_ringHom (R := adicCompletion K v)
show Continuous (RingHom.comp _ (Algebra.TensorProduct.includeRight.toRingHom))
convert (adicCompletionContinuousComapAlgHom A K L B v).cont using 1
ext
simp [adicCompletionTensorComapAlgHom, adicCompletionContinuousComapAlgHom]

noncomputable def adicCompletionComapAlgEquiv (v : HeightOneSpectrum A) :
(L ⊗[K] (HeightOneSpectrum.adicCompletion K v)) ≃ₐ[L]
Expand Down