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

Abstract

We compute the étale cohomology ring $H^{\ast }(\text{Spec }{\mathcal{O}}_K,\mathbb{Z}/n\mathbb{Z})$ where ${\mathcal{O}}_K$ is 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.

To be published in Research in Number Theory, 25 pages