Range tensor Adic Completion Integers To eq closure range algebra Map
IsDedekindDomain.HeightOneSpectrum.range_tensorAdicCompletionIntegersTo_eq_closure_range_algebraMap
Plain-language statement
The image of B ⊗[A] 𝓞_v in L ⊗[K] K_v is the closure of the image of B.
Exact Lean statement
lemma range_tensorAdicCompletionIntegersTo_eq_closure_range_algebraMap
[IsIntegralClosure B A L] [FiniteDimensional K L] :
Set.range (tensorAdicCompletionIntegersTo K L B v) =
closure (Set.range (algebraMap B (L ⊗[K] adicCompletion K v)))Formal artifact
Lean source
lemma range_tensorAdicCompletionIntegersTo_eq_closure_range_algebraMap [IsIntegralClosure B A L] [FiniteDimensional K L] : Set.range (tensorAdicCompletionIntegersTo K L B v) = closure (Set.range (algebraMap B (L ⊗[K] adicCompletion K v))) := by apply Set.Subset.antisymm · apply tensorAdicCompletionIntegersTo_range_subset_closure · apply closure_minimal · rintro _ ⟨b, rfl⟩ use b ⊗ₜ[A] 1 simp · apply IsClopen.isClosed apply tensorAdicCompletionIntegersTo_isClopen_range- Project
- Fermat's Last Theorem
- License
- Apache-2.0
- Commit
- 8dd808888295
- Source
- FLT/DedekindDomain/Completion/BaseChange.lean:488-499
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