nLab little etale topos

Definition

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

Then the category of sheaves $Sh(X_{et})$ is called the étale topos of $X$. (See there for more) This is the little topos-incarnation of $X$.

Related concepts

• étale site

• étale (infinity,1)-site