A Hermite-Minkowski type theorem of varieties over finite fields

As an application of P. Delgine's theorem (Esnault and Kerz in Acta Math. Vietnam. 37:531-562, 2012) on a finiteness of $l$-adic sheaves on a variety over a finite field, we show the finiteness of \'etale coverings of such a variety with given degree whose ramification bounded along an effective Cartier divisor. This can be thought of a higher dimensional analogue of the classical Hermite-Minkowski theorem.