  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.
