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Jun 2, 2020 at 13:39 comment added Laurent Moret-Bailly For a separated example, see my answer here: mathoverflow.net/q/194326
Jun 2, 2020 at 1:43 comment added Will Sawin After writing this I came up with a probably faster proof which is to compute the base change of the Weil restriction from $\mathbb R$ to $\mathbb C$ - it's the product of the affine line with two origins with itself - and check that one of the points lying over the origin doesn't have any Galois-invariant affine-neighborhood, which it would if the scheme descended from $\mathbb C$ to $\mathbb R$.
Jun 2, 2020 at 0:35 history answered Will Sawin CC BY-SA 4.0