The étale cohomology ring of the ring of integers of a number field

We compute the cohomology ring H∗(X,Z/nZ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^*(X,{{\mathbb {Z}}}/n{{\mathbb {Z}}})$$\end{document} for X the spectrum of the ring of integers of a number field K. As an application, we give a non-vanishing formula for an invariant defined by Minhyong Kim.