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Timeline for finite covering

Current License: CC BY-SA 3.0

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Jun 10, 2013 at 21:57 vote accept user34848
Jun 10, 2013 at 21:57 comment added user34848 I agree the covering $\Pi_{f}$ should be ramified. I misunderstood the article.
Jun 10, 2013 at 21:49 comment added Francesco Polizzi Obviously I mean $\Sigma \setminus p_1, p_2, p_3$
Jun 10, 2013 at 21:48 comment added Francesco Polizzi Sorry, but I really do not understand. The images of the loops $\gamma_i$ are non-trivial in $\mathbb{Z}_3$, so the map $\Pi_f$ is ramified at the points $p_i$, with stabilizer the whole of $\mathbb{Z}_3$. This is a very standard application of Riemann Existence Theorem. The cover over $\sigma \setminus p_1, p_2, p_3$ is étale, but the cover over $\Sigma$ is not.
Jun 10, 2013 at 21:43 comment added user34848 No, I am considering unramified covering $\Pi_{f}$
Jun 10, 2013 at 21:40 history edited Francesco Polizzi CC BY-SA 3.0
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Jun 10, 2013 at 21:36 comment added Francesco Polizzi You are welcome. But you meant "ramified", didn't you?
Jun 10, 2013 at 21:35 vote accept user34848
Jun 10, 2013 at 21:43
Jun 10, 2013 at 21:31 history answered Francesco Polizzi CC BY-SA 3.0