The \'etale cohomology ring of the ring of integers of a number field

Abstract

We compute the \'etale cohomology ring $H^*(\text{Spec } \mathcal{O}_K,\mathbb{Z}/n\mathbb{Z})$ 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.