# Troisi\`eme groupe de cohomologie non ramifi\'ee des hypersurfaces de Fano

## TL;DR

This paper proves the vanishing of the third unramified cohomology group for many Fano hypersurfaces over algebraically closed and finite fields, advancing understanding of their cohomological properties, with some cases still unresolved.

## Contribution

It establishes new vanishing results for third unramified cohomology of Fano hypersurfaces over various fields, extending previous knowledge in algebraic geometry.

## Key findings

- Vanishing of third unramified cohomology for many Fano hypersurfaces.
- Results over algebraically closed and finite fields.
- Open problem remains for cubic fourfolds over finite fields.

## Abstract

We establish the vanishing of the third unramified cohomology group for many types of Fano hypersurfaces in projective space over an algebraically closed field of arbitrary characteristic, and over a finite field. For cubic hypersurfaces over a finite field, the case of fourfolds remains open. --- Sur un corps alg\'ebriquement clos et sur un corps fini, on \'etablit de nouveaux r\'esultats d'annulation pour la cohomologie non ramifi\'ee de degr\'e 3 pour de nombreux types d'hypersurfaces de Fano. Le cas des hypersurfaces cubiques de dimension 4 sur un corps fini reste ouvert.