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Jun 22, 2019 at 2:04 comment added Puddles the turtle @Heavensfall, I originally read your original question as giving the size of $X(\mathbf{F}_{p^n})$ for all $p$ between $1$ and $N$. Fortunately, I think my original answer contains an answer to your actual question.
Jun 22, 2019 at 2:01 history edited Puddles the turtle CC BY-SA 4.0
Correcting for misreading of original question
Jun 21, 2019 at 21:46 comment added Heavensfall Thank you for your answer! I want to fix a N and consider (almost) all p. For example, if we take N=1, then my question is the same as asking whether on can recover Betti numbers from number of solution mod p for all prime p.
Jun 19, 2019 at 20:35 review First posts
Jun 19, 2019 at 21:01
Jun 19, 2019 at 20:35 history answered Puddles the turtle CC BY-SA 4.0