Is there a Seifert–van Kampen theorem for etale fondemental group? (for example for varieties over a non-algebraically closed field) Any example is welcome.
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3$\begingroup$ Is this SGA1 IX.5.1 (in this case where S' is the disjoint union of two open sets covering S)? $\endgroup$– Dylan WilsonCommented Dec 9, 2018 at 14:53
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3$\begingroup$ It is even easier than SvK for the topological fundamental group, as it simply amounts to etale descent for finite etale covers. $\endgroup$– Piotr AchingerCommented Dec 9, 2018 at 14:58
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6$\begingroup$ See [J. Stix, A general Seifert-Van Kampen theorem for algebraic fundamental groups, Publications of RIMS 42 (2006), no. 3, 763-786] $\endgroup$– user19475Commented Dec 9, 2018 at 15:32
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$\begingroup$ @Z.Zhou If possible, once you get some idea can you write down some rough sketch here... $\endgroup$– Praphulla KoushikCommented Dec 9, 2018 at 15:46
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