The Stacks project

Example 59.32.7. In the case $R = \mathbf{C}[[t]]$, the étale $R$-algebras are finite products of the trivial extension $R \to R$ and the extensions $R \to R[X, X^{-1}]/(X^ n-t)$. The latter ones factor through the open $D(t) \subset \mathop{\mathrm{Spec}}(R)$, so any étale covering can be refined by the covering $\{ \text{id} : \mathop{\mathrm{Spec}}(R) \to \mathop{\mathrm{Spec}}(R)\} $. We will see below that this is a somewhat general fact on étale coverings of spectra of henselian rings. This will show that higher étale cohomology of the spectrum of a strictly henselian ring is zero.