I went to different references on fundamental group on schemes. It is quite strange for me that the notion of fundamental group is only defined on connected scheme. Does anybody know why?
2026-05-04 11:08:01.1777892881
Why notion of fundamental group is defined only over a connected scheme?
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If we fix a point $x$ whose connected component is a proper subscheme, there is no way to capture the rest with the fiber functor at $x$. The correct notion would be the fundamental groupoid which should be well behaved for arbitrary schemes.