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Answer by Puddles the turtle for Number of solutions mod p and Betti numbers
Apologies; my first reading of the question (which confused an $n$ for a $p$) assumed you were only given $\#X(\mathbf{F}_p)$ for $p$ in a certain range. If you are given (almost) all the...
View ArticleAnswer by Will Sawin for Number of solutions mod p and Betti numbers
For the first claim, I think you want to also assume $X$ is smooth (away from some finite set of primes, not including $p$).For the second claim, again with the assumption that $X$ is smooth, this...
View ArticleNumber of solutions mod p and Betti numbers
Suppose $X$ is proper flat scheme over Sepc$\mathbb{Z}$. If $p$ is a large prime, then by Weil conjectures one can recover the Betti numbers of $X$ from the size of $X(\mathbb{F}_{p^n})$ for all $n$....
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