Corollary 3.6 . [00KC] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
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Corollary 3.6 .
The commutative diagram of homomorphisms of k k
( Spec ( V ∙ ( L ) ) ) an \textstyle{(\spec(V_{{\scriptscriptstyle\bullet}}(L)))^{\mathrm{an}}} 𝔐 ( V ^ ( L , ϕ aff ) ) \textstyle{\mathfrak{M}(\widehat{V}(L,\phi^{\mathrm{aff}}))\ignorespaces\ignorespaces\ignorespaces\ignorespaces} 𝔐 ( V ^ ∙ ( L , ϕ ) ) \textstyle{\mathfrak{M}(\widehat{V}_{{\scriptscriptstyle\bullet}}(L,\phi))\ignorespaces\ignorespaces\ignorespaces\ignorespaces} σ ∗ \scriptstyle{\sigma^{*}} ( Spec ( V ∙ ( L X | Y ) ) ) an \textstyle{(\spec(V_{{\scriptscriptstyle\bullet}}(L_{X|Y})))^{\mathrm{an}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces} i Y ∗ \scriptstyle{i_{Y}^{*}} 𝔐 ( V ^ ∙ ( L X | Y , ϕ X | Y aff ) ) \textstyle{\mathfrak{M}(\widehat{V}_{{\scriptscriptstyle\bullet}}(L_{X|Y},\phi_{X|Y}^{\mathrm{aff}}))\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces} i Y ( ϕ aff ) ∗ \scriptstyle{i_{Y}(\phi^{\mathrm{aff}})^{*}} 𝔐 ( V ^ ∙ ( L X | Y , ϕ X | Y ) ) \textstyle{\mathfrak{M}(\widehat{V}_{{\scriptscriptstyle\bullet}}(L_{X|Y},\phi_{X|Y}))\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces} σ | Y ∗ \scriptstyle{\sigma|_{Y}^{*}} i Y ( ϕ ) ∗ \scriptstyle{i_{Y}(\phi)^{*}}
All maps are closed. If the algebra seminorm ⦀ ⋅ ⦀ ϕ \vvvert\mathord{\cdot}\vvvert_{\phi}