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Anh Dũng Lê
Anh Dũng Lê
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I have a Galois cover $f \colon Y \rightarrow X$, i.e $f$ is finite étale and $deg(f) = Aut_X(Y)$. IsThe étale fundamental group $\pi_1(X,\bar{x})$ acts on the geometric fiber $Y_{\bar{x}}$, but is that also true that there is an action of the étale fundamental group $\pi_1(X,\bar{x})$ on $Y$? If yes how can I define such an action?

I have a Galois cover $f \colon Y \rightarrow X$, i.e $f$ is finite étale and $deg(f) = Aut_X(Y)$. Is that true that there is an action of the étale fundamental group $\pi_1(X,\bar{x})$ on $Y$? If yes how can I define such an action?

I have a Galois cover $f \colon Y \rightarrow X$, i.e $f$ is finite étale and $deg(f) = Aut_X(Y)$. The étale fundamental group $\pi_1(X,\bar{x})$ acts on the geometric fiber $Y_{\bar{x}}$, but is that also true that there is an action of the étale fundamental group $\pi_1(X,\bar{x})$ on $Y$? If yes how can I define such an action?

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Anh Dũng Lê
Anh Dũng Lê
  • 315
  • 1
  • 7

action of étale fundamental group on the cover

I have a Galois cover $f \colon Y \rightarrow X$, i.e $f$ is finite étale and $deg(f) = Aut_X(Y)$. Is that true that there is an action of the étale fundamental group $\pi_1(X,\bar{x})$ on $Y$? If yes how can I define such an action?