Base Change Right surjective
IsDedekindDomain.HeightOneSpectrum.adicCompletion.baseChangeRight_surjective
Plain-language statement
The canonical map L ⊗[K] K_v → ∏_{w|v} L_w is surjective.
Exact Lean statement
lemma baseChangeRight_surjective [FiniteDimensional K L] :
Function.Surjective (baseChangeRight K L B v)Formal artifact
Lean source
lemma baseChangeRight_surjective [FiniteDimensional K L] : Function.Surjective (baseChangeRight K L B v) := by let s := (baseChangeRight K L B v).toLinearMap.range have isClosed : IsClosed s.carrier := Submodule.closed_of_finiteDimensional (E := (w : Extension B v) → adicCompletion L w.val) s rw [← AlgHom.coe_toLinearMap, ← LinearMap.range_eq_top, Submodule.eq_top_iff'] simp_rw [← Submodule.mem_toAddSubmonoid, ← AddSubmonoid.mem_toSubsemigroup, ← AddSubsemigroup.mem_carrier] have denseL : DenseRange (algebraMap L ((w : Extension B v) → adicCompletion L w.val)) := by have := Extension.finite A K L B v exact denseRange_of_prodAlgebraMap _ Subtype.val_injective rw [← isClosed.closure_eq] apply Dense.mono _ denseL rintro _ ⟨l, rfl⟩ use (l ⊗ₜ 1) simp- Project
- Fermat's Last Theorem
- License
- Apache-2.0
- Commit
- 8dd808888295
- Source
- FLT/DedekindDomain/Completion/BaseChange.lean:297-312
Reuse this declaration
Bring the exact result into your workflow
The import identifies the source module. Your project still needs the pinned package dependency shown on this page.
What this badge means
This completion status comes from the project or community source. It has not yet been represented here as an independent rebuild and axiom audit.
Continue in this project
Related declarations
Eq finsum quotient out of bij On
AbstractHeckeOperator.eq_finsum_quotient_out_of_bijOn'
Plain-language statement
If a is fixed by V then ∑ᶠ g ∈ s, g • a is independent of the choice s of coset representatives in G for a subset of G ⧸ V
Source project: Fermat's Last Theorem
Person-level attribution pending.
Comm Group no compact automorphisms
CommGroup.no_compact_automorphisms
Plain-language statement
A connected compact Hausdorff abelian topological group does not admit a nontrivial compact group of automorphisms.
Source project: Fermat's Last Theorem
Person-level attribution pending.
Fermat Last Theorem of p ge 5
FermatLastTheorem.of_p_ge_5
Plain-language statement
If Fermat's Last Theorem is true for primes p ≥ 5, then FLT is true.
Source project: Fermat's Last Theorem
Person-level attribution pending.