nLab lisse-étale site

Idea

The lisse-étale site of a scheme $X$ is the category of $U \to X$ which are smooth morphisms with coverings defined as in the étale site.

The lisse-étale site is not so well-behaved, but it is used in the study of algebraic stacks in order to have a site with more affine opens, hence better suited for the discussion of quasicoherent sheaves.

References

• The Stacks Project, 79.11. The lisse-étale and the flat-fppf sites