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May 13, 2014 at 0:57 answer added S. Carnahan timeline score: 1
May 9, 2014 at 22:40 history edited Kevin.lijh CC BY-SA 3.0
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May 9, 2014 at 22:03 comment added Will Chen Well any definition of a universal etale cover will generally not be finite. In your setting the universal etale cover is probably referring to the inverse limit over all finite etale covers, or perhaps the pro-object described by the inverse system over all finite etale covers, so if your space admits covers of arbitrarily large degree, this "universal cover" won't be finite. This is described in SGA 1, section V (though in french). The universal cover is described as the "pro-objet fondamental".
May 9, 2014 at 20:36 history edited Ricardo Andrade
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May 9, 2014 at 20:31 history edited Kevin.lijh CC BY-SA 3.0
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May 9, 2014 at 20:21 history asked Kevin.lijh CC BY-SA 3.0