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May 12, 2019 at 14:07 comment added Zhiyu For betti numbers modulo $\ell$ (which is equal to the original Betti number for large $\ell$), see arxiv.org/abs/1304.5376.
May 12, 2019 at 7:12 comment added Daniel Loughran This paper discusses this question for $\ell$-adic cohomology: www-math.mit.edu/~poonen/papers/compute_ns.pdf
May 12, 2019 at 6:58 history asked user138661 CC BY-SA 4.0