The proétale topology on schemes, introduced by Bhatt and Scholze, provides a convenient framework for capturing the topological behavior of coefficient rings such as $\mathbb Z_\ell$ and $\mathbb Q_\ell$ in étale cohomology. While being sufficient for many purposes, general proétale sheaves on schemes can be quite wild, and there is no well-behaved formalism of six operations.

In this talk, we will introduce categories of solid proétale sheaves on schemes that aim to address this issue by adapting ideas of Fargues and Scholze. We will show that these categories admit a full six-functor formalism while remaining large enough to include all objects typically encountered in practice. We achieve this by comparing them to a suitable theory of proétale motives, which may be of independent interest. This work is joint with Raphaël Ruimy and Swann Tubach.