# Is there a Seifert–van Kampen theorem for etale fondemental group?

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.

• Is this SGA1 IX.5.1 (in this case where S' is the disjoint union of two open sets covering S)? – Dylan Wilson Dec 9 '18 at 14:53
• It is even easier than SvK for the topological fundamental group, as it simply amounts to etale descent for finite etale covers. – Piotr Achinger Dec 9 '18 at 14:58
• See [J. Stix, A general Seifert-Van Kampen theorem for algebraic fundamental groups, Publications of RIMS 42 (2006), no. 3, 763-786] – user19475 Dec 9 '18 at 15:32
• @Z.Zhou If possible, once you get some idea can you write down some rough sketch here... – Praphulla Koushik Dec 9 '18 at 15:46