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Mikhail
Mikhail
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Suppose that $A$ is a reduced finitely generated algebra over a field and $\mathfrak{m}\subset A$ is a maximal ideal. Is it true that the localization $A_{\mathfrak{m}}$ is analytically unramified, i.e. the completion $$ \widehat{A_{\mathfrak{m}}} = \lim\limits_{\infty\leftarrow n}A_{\mathfrak{m}}/\mathfrak{m}^n $$$$ \widehat{A_{\mathfrak{m}}} = \lim\limits_{\infty\leftarrow n}A_{\mathfrak{m}}/(\mathfrak{m}A_{\mathfrak{m}})^n $$ is reduced?

Suppose that $A$ is a reduced finitely generated algebra over a field and $\mathfrak{m}\subset A$ is a maximal ideal. Is it true that the localization $A_{\mathfrak{m}}$ is analytically unramified, i.e. the completion $$ \widehat{A_{\mathfrak{m}}} = \lim\limits_{\infty\leftarrow n}A_{\mathfrak{m}}/\mathfrak{m}^n $$ is reduced?

Suppose that $A$ is a reduced finitely generated algebra over a field and $\mathfrak{m}\subset A$ is a maximal ideal. Is it true that the localization $A_{\mathfrak{m}}$ is analytically unramified, i.e. the completion $$ \widehat{A_{\mathfrak{m}}} = \lim\limits_{\infty\leftarrow n}A_{\mathfrak{m}}/(\mathfrak{m}A_{\mathfrak{m}})^n $$ is reduced?

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Mikhail
Mikhail
  • 465
  • 2
  • 6

Is a localization of a reduced finitely generated algebra analytically unramified?

Suppose that $A$ is a reduced finitely generated algebra over a field and $\mathfrak{m}\subset A$ is a maximal ideal. Is it true that the localization $A_{\mathfrak{m}}$ is analytically unramified, i.e. the completion $$ \widehat{A_{\mathfrak{m}}} = \lim\limits_{\infty\leftarrow n}A_{\mathfrak{m}}/\mathfrak{m}^n $$ is reduced?