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Jul 6, 2018 at 10:18 history edited Michael Albanese CC BY-SA 4.0
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Jul 6, 2018 at 10:13 comment added Michael Albanese You are absolutely right. I will edit accordingly.
Jul 6, 2018 at 10:06 comment added Will Sawin Isn't your question at the end answered in the negative by the existence of complex projective spaces, but not rational projective planes in all even dimensions?
Jul 6, 2018 at 10:01 history answered Michael Albanese CC BY-SA 4.0