# GAeL XXII

### Bhargav Bhatt

"h-topology and applications"

These lectures will introduce Voevodsky's $$h$$-topology and some variants. Our focus will be on geometric applications (such as Hodge theory and singularities)

### Hélène Esnault

"Miscellaneous on rational points and fundamental groups"

The guiding conjecture of the lectures is the $$C_1$$ conjecture, due to Lang-Manin-Kollár, predicting that a rationally connected variety over a $$C_1$$ field has a rational point (with some separability assumption in positive characteristic). The essential case where it is still unknown is over the maximal unramified extension of $$\mathbb{Q}_p$$. We will discuss various aspects of the problem, and related questions.