In the lecture note of bhatt from arizona winter school 2017, there is an exercise which claims if X is a proper somooth scheme defined over $\mathbb{Z}[1/N]$ and if there is a polynomial $P$ such that for every prime $p$ coprime to $N$ we have $X(F_p)=P(p)$ then the hodge numbers $h^{i,j}=0,i\not =j $ I don't know how to attack this problem because if you want to use zeta functions and weil conjectures you need the number of point of X over all finite fields. But I don't have any counter example. So is there a typo in this exercise or can someone hint how to prove the claim