Arithmetic cohomology over finite fields and special values of \(\zeta\)-functions (Q2496922)

In the present paper, the author, using ideas of Voevodsky, constructs a modified version \(H^i_c(X_{\text{ar}},\mathbb Z(n))\) of Weil-étale cohomology, which he calls arithmetic cohomology (with compact support). Arithmetic cohomology groups are expected to be finitely generated and related to special values of \(\zeta\)-functions for every separated scheme of finite type over a finite field and generalize Lichtenbaum's Weil-étale cohomology groups defined for smooth and projective schemes.