nLab
little etale topos

Definition

For $X$ a scheme or more generally an algebraic stack, let $X_{\mathrm{et}}$ be its small étale site: the full subcategory of the slice category $\mathrm{Aff}/X$ on the étale morphisms equipped with the induced étale topology.

Then the category of sheaves $\mathrm{Sh}(X_{\mathrm{et}})$ is called the étale topos of $X$.

This is the little topos-incarnation of $X$.

Related concepts

• étale site

• étale (infinity,1)-site