Étale cohomology of arithmetic schemes and zeta values of arithmetic surfaces
arXiv:2001.09845
Abstract
In this paper, we give an approach to the zeta values of a (proper regular) arithmetic scheme X at the integers r>=d:=dim(X), using étale cohomology of X with Q_p(r) and Z_p(r)-coefficients.
arXiv comment62 pages. Remark 2.2 has been added. Proposition 7.3 has been modified. Some details of the proof of Lemma 7.9 have been improved, and many typos have been corrected. To appear in Journal of Number Theory