Hello,

I remember reading that if $X/\mathbf F_q$ is a projective smooth global complete intersection, then the characteristic polynomial of the $\mathbf F_q$-linear Frobenius of $X$ on $H^i_{et}(X\otimes\overline{\mathbf F_q},\mathbf Q_l)$, $l\nmid q$, has integer coefficients and is independent of $l$.

How does one prove this fact?

Thanks