分野別セミナー

We show the finiteness of etale coverings of a variety over a finite field with given degree whose ramification bounded along an effective Cartier divisor. The proof is an application of P. Deligne’s theorem (H. Esnault and M. Kerz in Acta Math. Vietnam. 37:531-562, 2012) on a finiteness of l-adic sheaves with restricted ramification. By applying our result to a smooth curve over a finite field, one obtain a function field analogue of the classical Hermite-Minkowski theorem.