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Jul 26, 2015 at 14:53 vote accept Alex Youcis
Jul 26, 2015 at 9:44 answer added Piotr Achinger timeline score: 9
Jul 25, 2015 at 20:24 comment added Niels Question 2 is reminiscent of the Malcev-Grothendieck theorem : if the étale fundamental group of a smooth complex projective variety is trivial, then there is no non-trivial bundle with a flat connection. See the introduction of arxiv.org/abs/1112.4603 .
Jul 25, 2015 at 15:53 answer added Donu Arapura timeline score: 13
Jul 25, 2015 at 15:15 history edited Alex Youcis CC BY-SA 3.0
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Jul 25, 2015 at 15:10 comment added Donu Arapura I strongly suspect that the main question is false, but I'll need to think more about it. There is a typo in 2 by the way. 2 and 3 are open as far as I know. Although there exists smooth projective varieties with non residually finite fundamental groups (Toledo,...).
Jul 25, 2015 at 14:44 comment added Alex Youcis @potentiallydense I may be the potentially dense one. :) Thanks for pointing that out.
Jul 25, 2015 at 14:43 history edited Alex Youcis CC BY-SA 3.0
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Jul 25, 2015 at 14:41 history asked Alex Youcis CC BY-SA 3.0